Yet seriously... what is there to fight over?
Ideological differences, of course. USA, Russia and China all want to be hegemonies, to dominate and rule over the world. Thus, they're natural enemies to each other.
They've all, to some extent, become
regional hegemonies* though... and based on some theories, that's the most stable position we can be in, outside of a full global hegemony which, by the same theories is impossible to achieve simply based on the scale.
That doesn't mean fighting will stop once these hegemonies have established themselves and bumped up against each other, but instabilities will minimize as the powers balance each other out. The problem we have now is that Russia is in an odd position. The US or NATO based regional hegemony has squeezed in through Europe on one side, and China is snuggled right up against them on the other. Russia has lost a lot since the heyday of the Soviet Union. They're left with a relatively economically weak main country, and no-where to expand/consolidate but into NATO territory or south into the Middle East. We saw this instability manifest itself violently over the last decade or so, first with Georgia then Ukraine (and I might be missing something or other in there, but those two spring to mind without further research.) Attention seems to be focused on the middle east now as far as overt power. But they're still destabilizing things with their covert and diplomatic actions as well.
Granted this is all my simplified and novice interpretation based upon my reading of one theory which I don't completely agree with. So add salt as desired.
*Yes, John Mearsheimer was required reading in my international politics classes in Uni. Agree with him or not, but he makes a good argument.