This has been bugging me for a while. Why lose sleep over it? I'm not, but I can't help thinking that the US will not allow this to happen, just like they didn't allow the Japanese to overtake them as the #1 true superpower. This was done covertly (not by the military!) and you can bet that the plans are on the table.
Personally I don't really care which country 'dominates' the world. I like the Chinese anyhow, and it's a no-brainer that some (one) country/civilization always will dominate. But I just don't think the Chinese will dominate, just like the Japanese didn't; that was on the cards when a byproduct of 80s Reagan administration meant that Japan's currency appreciated thus constricting their economy. Their people became less obedient, less efficient and more radical and this (in the coming decades) is highly likely in China too.
The Chinese are kind-of where the Japanese were in the 60's and 70s; low wages etc (not referring to GDP growth per annum necessarily). The Japanese were an up-and-coming emerging force and by the mid to late 80 they were viewed as a powerful rival, buying-up American corporations etc. But this is only part of the picture. Japan would never have a more powerful military force as the post WWII era prevented them from having an aggressive military presence. China's military will never be as advance as the US's. The Americans will hate me for this, but the US's military and defense must be light years ahead of any other nations.
China (which just overtook Japan as the #2 economy) is viewed as an unstoppable force in all respects (economy, militarily etc). But there will always be a gap between the US and the rest of the world. China may have more money than Japan right now, but there still is a gap between the two as Japan still has a far more sophisticated economy and it probably will in a decade, even if China has twice the money Japan has. The key is how sophisticated will China's economy get? With the current communist model, not sophisticated at all.
China's inability to grasp the western, capitalist model and its inevitably strong currency will be key to China's failure to dominate the world stage like most people think.
In fact, if the Chinese Yuan wasn't pegged to the US dollar it would be close to twice as strong as it is today. So what? Well for starters you wouldn't buy as many products from China (this may be a good thing for the US). A stronger currency puts lots of pressure on (the need for higher) wages too. Even if the Chinese economy outgrows the US's, like nearly everyone thinks, there will still be a gap between the US and China.
No communist state has ever claimed the top prize and there's a good reason for this; they don't have free, dynamic, strong and sometimes chaotic markets. In fact, not being a true capitalist state means that China will not be able to control and to positively or negatively influence markets around the world. Those that can directly influence markets around the world will always have an edge on the rest and the US will not let this one out of their sights. Don't forget that even when the US economy suffered it was still the most influential market by far; as hard as it is to stomach, the downturn in the US (domestic) economy has meant the Fed's printing presses to run hot and the US dollar to drop, which helps exports. This is why several US companies that export are at record highs! The shift has been for US companies to extend their influence in overseas markets (including China) and this could be part of a grander long-term plan to remain the dominant force.
Westernization will to some extent spread throughout China like a plague in the coming decades, not because there's anything wrong with our model but because they aren't use to it and the western model will conflict with their established and contrary ways. You need to be fully exposed to all aspects of the western capitalistic model for decades to fully understand/relate to it. And the US will be way to far ahead by then and China will be playing an endless game of catch-up.
Without becoming western, China will not be able to become the dominant player in the world, even if they collectively become a wealthier nation than the US; as this is bound to happen. If they try to become western it will fail and if they don't try to become western, China will become an incredibly wealthy nation but with very little power and influence in proportion to their wealth. In fact, its influence will not surpass that of the United States.
If they become western (which I really can't see happening) then they run the risk of being broken up from within. This could come in the form of several provinces wanting independence (hard to believe now) to instability being created and reinforced from outside their borders; just like its happening in the middle east and other parts of the world (more likely).
The bottom line is China is currently becoming a wealthy nation by artificial means (by manipulating their currency to have an advantage in trade (this is causing inflation to run riot), by establishing and reinforcing a cheap-labor environment (won't last), by controlling all aspects of Chinese life (won't last)). But in order to be a true player in the world stage it will need to loosen its grip on all of the above. But with freedom comes chaos. This is the natural order of things. Ironic, isn't it? The Chinese won't know what hit them, but you can bet that there are several interested parties really wanting this to happen; just like they did with Japan in the 80s.