What about this? Suppose Hitler never invaded the Soviet Union, and instead commenced Operation Sea Lion, without American help, Britain would have not beat back the krauts. So we see Nazi-dominated Europe, Soviet-dominated Asia, Japanese-dominated Pacific, and Italian-dominated Africa? Although Hitler's blind hatred for bolshevism probably would have prevented this from happening, could this have happened if FDR died?
As you say, I don't think it ever would have happened; Hitler showed little capacity for the kind of strategic restraint this would have required. But, militarily speaking, it could have happened, though I wonder of China's fate and I think any invasion of Britain would have taken years of planning and buildup. It would have ensured that the U.S. stayed isolationist, or simply sought to play off the three powers against one another unless provoked. It's hard to imagine the U.S. gravitating heavily towards any of those powers, save for a radical change in political mentality or some kind of perceived economic necessity (oil?).
Internally, though, all three would have had serious problems. Hitler would have had to handle continued resistance and guerrilla warfare, especially in France and Britain. Many refugees would have fled to Canada or the Soviet Union (depending on their political views) and funded resistance from there. The USSR would have had issues with the Middle East (as in reality, though they probably would have competed with Germany here) and in China. Much of Asia would be outside of their influence for some time; I don't think they could have consolidated it very rapidly. Japan would have similar problems in China (presuming they maintained a position there) and Southeast Asia.
And what of Africa? Do some pieces escape colonialism? I cannot imagine a war-weary Germany occupying the entire continent (or even most of it). Australia and New Zealand are another question mark; I don't think Japan would have been able to dominate them, at least not physically.