In 1940, Italy declared war on the Western powers and entered WW2. On paper it was an act of idiocy. Their military was unready. Their colonies were not properly provisioned. The bulk of their merchant marine was at sea and thus immediately lost to the British. The sole intelligent reason for this act was a cool calculation that France was about to fall. Reasoning that the British Empire would not fight on without its continental sword (the French Army), Italy expected there to be a peace conference. Their few weeks of combat would buy them a seat at the conference, which in turn would probably result in Italy picking up some new colonial territory, and, perhaps, some border adjustments with France or Yugoslavia.
From Tiny Acorns Grow an Oak by Scott PalterNeedless to say, the calculation was completely in error. The war would cost Italy all of her colonies and the destruction of the body of the country when it became a war zone for the final two years of the European struggle. All of this would occur because of a miscalculation in British intentions. Let us presume that Churchill took time out from the chaos of France's collapse to make VERY clear to the Italians that this was the end of a phase of the war, rather than an end of the war. Let us presume that the French made some minor territorial concessions to Italy (the Azzou strip in northern Chad and some Saharan sand on the Libyan - Algerian border). Italy stays neutral.
The early changes in the war are subtle. The later are far grander.
There are no changes in the Battle of Britain or Battle of the Atlantic. Italy made little contribution to either. Britain would have needed large naval forces to watch a neutral Italy whose government was capable of intervention at any moment. However, there are no campaigns in North Africa, Greece, Syria, Iraq or East Africa. The British Army does not suffer these losses or gain this combat experience. Except for commando raids, Britain is not engaged in a ground war between the Fall of France and Pearl Harbor. The RAF does not have to build a Desert Air Force. The troops and planes not so used are available to garrison Burma and Malaya. We will return to the results of this shortly.Rommel's three divisions are a minor addition to the invasion of Russia. The addition of the air elements sent to the Mediterranean is more noticeable. The biggest difference is the absence of a Balkan campaign. In OTL, Italy invades Greece in 1940. They fail miserably at it. This forces Germany to take a Balkan detour that winds up including Yugoslavia and Crete. In this TL none of this occurs. Yugoslavia and Bulgaria are forced into the Tripartite Pact over the winter of 1940-41 on very mild terms. No German garrisons are needed in either. Greece is allowed its neutrality as long as trade with Germany is continued (same as Turkey and Sweden in OTL).
In OTL the Balkan adventure postponed Barbarossa by two weeks and added much wear and tear on the trucks and men making the long roundtrip. It bled off a German army (12th) left behind in garrisons from Belgrade to Athens. It also destroyed the German airborne forces on Crete.
A two week earlier start does not take Moscow or win the war in 1941. Neither the ten extra divisions (DAK plus 12th Army) nor the fewer vehicle breakdowns make Moscow any nearer to Warsaw and Konigsburg. A German win in 1941 requires a very different set of changes than Italian neutrality. However, the extra two weeks do see a German Army less burned out when it is repulsed before (or perhaps in the streets of) Moscow in early December of 1941. At each of the three German advances, the rear has been better swept (fewer Red Army remnants to form partisans), the supply forces have had a little more time to do their work, and the giant number of abandoned weapons have been better collected.
To do we will add an Italian Expeditionary Force ( say six divisions of Blackshirts and Young Fascists, which is what was sent to Spain in the 1930's). Italy does not declare war on Russia. These are ?volunteers' like the Spanish Blue Division (party to party as opposed to state to state to use the usual Communist terminology). To this will be added a Corps of White Russian volunteers from Yugoslavia, also under Italian command. These men are neither trained nor armed for frontline service. However, they are quite capable of policing up the vast hordes of Russian prisoners captured in the great encirclement battles of 1941. The Italians will drive this herd to the railheads, where they are shipped to Italy as war booty (slaves). A good bit of Russian equipment will follow, bringing the Italian military to a less unready state. The Italians also lack the German racial hatred of the Easterners. They will extensively recruit among the prisoners and locals. The net effect is that the eight Italo-Yugoslav divisions will be almost to corps strength each by the end of 1941.
So the retreat from Moscow never develops into the semicollapse of OTL. This results in fewer German losses, higher Russian ones and an earlier burnout of the Russian offensive. Part of this is the large Italian force garrisoning the towns to the rear of Army Group Center. Part of this is the better state of the German lines of communication and depots. The largest single change is that Kesselring's Second Air Fleet does not have to be pulled out of Belarus to bail out the Desert War.
So the spring - summer of 1942 finds a marginally stronger German Army in the East and a marginally weaker Russian one. We will return to the effects of this after our Asiatic detour promised above.
In OTL an overstretched British Empire made the decision to give priority to absolutely everything over the defense of Burma, Malaya, the East Indies and the South Seas (Australia, New Zealand, etc.). Without a North African war, the best of the Indian Army and the bulk of the Anzac forces are not in the Mediterranean. As is, Malaya and Burma were near run things. In this TL, the initial assaults on Malaya and Burma are repulsed.
The East Indies will still fall, but more slowly. It will take until the end of 1942 to finish them and Malaya off. Burma will stay in Allied hands. Now the results of this will seem perverse. A better British general in Singapore, a larger British Fleet, and a much larger RAF contingent will mean that in the end the British Empire will lose many more ships, men and planes. Essentially, the British simply couldn't stand up to the Japanese Navy or Air Force in this period. A Cunningham or Auchinlek in Singapore in place of Wavell and Percival could blunt the Japanese Army and bleed them badly. He could not change the air-naval equation. That equation determined the ultimate logistical result of the campaign.
However, with the Japanese carrier fleet tied up taking the East Indies and Malaya, Japan never gets "victory disease". In OTL they were wildly successful at first. This caused them to get overconfident and change their strategy. Instead of fortifying their conquests and waiting to attrit the American counterattack, they attacked in all directions. The result was a series of campaigns (Coral Sea, Midway, Solomons, Papua - New Guinea) that basically destroyed the elite prewar naval and air units.
Instead here the much slower initial advance keeps them in their proper hedgehog. This will make the Pacific War much longer and bloodier. It will also means that Bataan lasts somewhat longer as the Japanese concentrate on finishing off the East Indies first. This gets more US ground and air units sent to Australia. However, it also means that after securing Australia, Port Mosby, Guadalcanal and the South Sea string of bases, the Pacific War essentially grinds to a halt in early 1943. Until America's new carrier fleet becomes available in 1944, the Allies lack the power to go further. So 1943 is a sea - air sparring contest in which neither side takes major risks.
Back to Russia: the primary problem with the German summer offensive is again geography plus the higher command's insanity in conducting a street fight in Stalingrad. This will not change. However, the equipment seized in 1941 will make the Italian 8th and Hungarian 2nd Armies marginally stronger. It will also provide marginally more reserves behind the Rumanians. Stalingrad will still be encircled. The retreat from the Caucasus will still be necessary.
What will be different then is that there will not be a companion disaster in North Africa. The Allied occupation of French Northwest Africa will open the Mediterranean more easily to Allied shipping. It will not require a Panzer Army to be sent to Tunis or 60% of Germany's long-range aircraft. Instead those units will be available to the Don Front. There will be no breakout from Stalingrad (Hitler wouldn't have permitted it). There will be less of a Russian advance and a bigger backhand blow by Manstein. On the margin the Germans will be stronger, the Russians weaker.
Without a Mediterranean front in 1942-43, the Allies will not be able to withstand Russian pressure to do something besides air raids. In OTL the Allies fought major 1943 campaigns in Burma, New Guinea, the Solomons, Tunis, Sicily and southern Italy. None of those happen here. Instead there is a May 1943 invasion of France.
There is no Atlantic Wall. The defenses of the beaches between the major ports was Rommel's doing in late 1943-44. So the invasion force gets ashore more easily. There is a smaller German garrison in France so the lodgment goes more easily and Cherbourg falls faster. The good luck ends there. Germany has more reserves and is less heavily attrited is this TL. The American and British armies are much greener. There is no Normandy breakout.
Instead there is a slow attritional grind forward, with the Combined Bomber Force being repeatedly used in a ground support role to blow holes in the German lines (of the type from the Cobra attack in OTL). This in turn destroys the German Air Force faster as the attritional fighter battles take place nearer to England. Instead of the Lw fighter arm collapsing in the first months of 1944, it is bled to death here in the summer and fall of 1943 over France.
Normandy does appear to help the Russians. The Kursk offensive is never made. This actually hurts. Without Kursk and without an Italian front soaking up two German armies (and the defection of Italian forces in Yugoslavia soaking up two more), the Germans have sufficient reserves to make the reconquest of Ukraine slower and more expensive. The disparity of forces and the ongoing drain of Normandy means they lose, but in takes all of 1944 to clear Ukraine and retake Smolensk (one year behind OTL).
In the meantime, by the end of 1943 the Western Allies have cut off Brittany and enlarged their bridgehead to the Lower Seine but are nowhere near Paris. The bomber attacks on the western German cities are much less than OTL but still enough to cause pain. Speer hits on the idea of relocating some plants to Italy to take advantage of its neutral status. Italy has no air raids, a friendly government and those millions of Russian POW's as force laborers. It has also taken in millions of other refugees from the Nazis so it has the potential for major industrial production given German help with machine tools, technicians, etc. Italy begins force draft industrialization. The Allies are angry but do not need another front.
The Allies spend 1944 clearing France to the Somme and Meuse, aided by secondary invasions in Calais and Provence. In the Pacific, the Japanese get their predicted climatic naval battles in the Marianas. Essentially both fleets destroy each other while the American ground forces take the islands at extremely high cost. This is what happened in OTL in the Solomons. Then, as here, the US can build more ships and Japan cannot. So we have no major offensive in the southwest Pacific or Burma, but rather bloodbaths at Wake, the Marianas and Iwo, followed by a submarine blockade of Japan. Japan will still make its 1944-45 offensive in China that drives Chiang effectively out of the war. The difference here is that with the Burma Road open, a substantial part of the Chinese Army retreats in northern Burma, where the Allies rebuild and retrain it (Chiang will have many times as many top notch divisions in the Chinese Civil War).
1945 sees the Allies slog forward to and across the Rhine. Stalin's forces take Rumania, Belarus and the Baltic States but come up short at the Vistula and East Prussian border. The Combined Bomber force keeps hammering the German transport net and synthetic petrol facilities. Starting in August they have nukes to add - 3 the first month and two a month thereafter. By the end of 1945, Germany still has two coherent fronts, but is bleeding to death internally. Jets, V-2's and other wonder weapons cannot make up for a collapsed industrial and transport base, no food and no fuel for the weapons. The German resistance starts to fragment in early 1946. Stalin still wins the race to Berlin (May 1946) but the West beats him to Prague and Vienna. The war in Europe ends in June of 1946 without a formal surrender. Millions of Germans and Hungarians seek sanctuary in Italy. WW2 in Europe ends with an extra ten million dead, far more damage and a much stronger Italy with a correspondingly weaker Britain, France and Russia.
In the Pacific, 1945 has seen the Americans take Okinowa and Pusan to tighten the blockade of Japan. American fire bombers have leveled the cities. Millions of Japanese have starved. However, the major ground offensives we had in the Pacific have been diverted to meet the needs of a longer and far more expensive European campaign. By early 1946 the Japanese Court and most of the Army Higher command have relocated to the Asian mainland to escape the famine in the Home Islands. The social structure of the abandoned Japanese homeland disintegrates. The Emperor dies in an air raid on Munkden. The Army fights on. We and the Russians redeploy from Europe. When the Russian invasion of Manchuria destroys the main Japanese armies (August 1946), the Home Islands surrender to us. Japan does not end the war so much as disintegrate. By now the death toll from starvation and disease is over ten million. Russia overruns North China and most of Korea. They set up friendly regimes (Mao and Kim) keeping the lands they have taken. Chiang essentially gets the Yangtse Valley and the South. He spends the balance of the decade suppressing Maoists in his zone. China is effectively partitioned.