Impossible?! It is literally beyond that as a "what-if" Some of the problems: Germany lacks a navy. It will take them at least a decade of concentrated effort to produce a viable one and then, largely at the expense of their army (ie big navy smaller army). Even after producing a navy capable of engaging the US at sea (to ensure their forces make it across the Atlantic) they are then faced with the very real (and certain) threat of a "reverse" U-boat campaign by the US on their shipping. This will require further heavy investment in naval forces and aircraft to counter. The US, alone, spent about $11 billion on stopping German U-boats. The German economy could never, even with the infusion of captured area economic input, take a hit that big. Next, the Germans are faced with a nation that has roughly the same population as the Soviet Union. As a land power on the North American continent the US Army could have easily reached 200 to 300 divisions if necessary. The US has internally the resources to make this happen. On the flip side, the Germans are now faced with having to ship their forces and supplies over thousands of miles of ocean to fight. It is doubtful they could put anything close to enough troops ashore to successfully fight the US. Then there is simply the size of the US. Again, the Germans are facing a huge problem just in trying to take and secure such a large land mass. Some areas would be exceedingly difficult for the Germans to operate in too. Invading from Mexico for example means primarily trying to cross what is mostly low desert with very few roads and even fewer north - south oriented ones. They would also be faced in Arizona with range and basin terrain, a huge defense advantage. In New Mexico it is Rocky Mountian terrain. West Texas is just as bad. Scrub desert, no roads, no towns to speak of, etc. Southern California is a major bastion of the US military, even at the time. It would be resolutely defended no doubt. Of course, the US would not have set idly by while the Germans built up an army in Mexico either. Major ports? Virtually all are fairly well defended by coastal defenses. The Germans would have virtually no information on beach conditions for amphibious assaults, and very little experiance in performing them. Air power would be another problem. The Luftwaffe designed aircraft with ranges suitable for combat in Europe. In the US, as in the Soviet Union, these aircraft are going to be of limited use due to their short ranges. Basically, the Germans lack the economy and military competence necessary to wage a truly global war. I doubt they could have managed to do anything against the US of truly worthwhile result to them. As for Japan, this is just ridiculious. The Japanese are hopeless in this example.