I actually wrote a paper in school on this very question, except in my paper China was involved in the take over not just Russia and the USA. In my
report all three country's would theoretically concentrate on the middle east first for obvious reasons.
Russia would take Europe and most all the country's on its border.
China would take all of south east Asia including japan and Australia.
The USA would naturally control south America and Canada. As for the middle east it would be split up between the three country's.
And as for Africa, I never did come up with a good conclusion. I suppose it would be split up or fought over. Which would lead to the middle east
being fought over. Alas nothing would be solved and the world would be in the same situation it is currently.