There would be eventual competition between all three superpowers. I've said before that each country will play off one another when it is convenient. Friends one day, enemies in another. It's been mentioned here that it will be less ideologically motivated (Capitalism vs. Communism) and more of a type of "Great Game". Japan, however, would be more inclined to have some kind of ideology, since that's what made them a threat OTL (Japanese Supremacy, Divinity Will of the Emperor, etc.)I'm not particularly convinced that a true cold war like OTL would be inevitable really anywhere. There'd be an uneasy peace most likely but Germany and America have no real reason to antagonize each other and Japan doesn't have global ambitions or influence.
More than likely each of the three would just stick to their own spheres of influence, America's I see including Australia and New Zealand but not much else outside of the Americas.
This is almost exactly my viewpoint, too. However, I think the Danish and Dutch would still retain their Caribbean islands.Probably just the Caribbean would go to U.S.; which it really de fact possessed since 1917 (not counting the 1941-1943 period that the British re-established a presence there). The other parts of the British Empire would either fall under Germany (Africa) and Japan (Asia), lean toward the U.S. (Australia/New Zealand), or break out into open conflict (India).
Any thoughts on French Guiana?