I think the days of any one one entity having "world supremacy" are basically over. China will never have the ability to project force in the manner the winners of WWII were able to during the post war era. I don't see any other entity having much of a chance either. If we can't do it they certainly won't be able.
At most the Chinese economy will move from the periphery and being an industrial producer to joining the developed nations at hte core of the global economic system as a capital intensive financial power.
I don't think projecting military force much interests the Chinese. Their area of expertise lies elsewhere.