This isn't really a TL, or even a brainstorm topic for a TL, but the outcome of this topic will probably influence some future TL I will do someday.
As many people know, white Americans in the 19th century had a great tendency to judge people based on the color of their skin and their ethnic background. Sometimes this was just a cultural proclivity (WASP 'racism' against Catholic Irishmen), and sometimes there were more...mundane reasons behind this prejudice. One group which suffered from the latter were Asian, and especially Chinese, immigrant laborers. The stereotype that Chinese workers were extremely hard working, very frugal, and capable of putting up with terrible living and working conditions, genuinely scared many white workers who did not want to see their own living standards reduced if forced to compete with Chinese laborers.
The outcome of this was the Chinese Exclusion Act, and a penumbra of similar laws, treaties, and understandings that kept Korean, Japanese, and other East Asian immigrants out of the US.
However, and ignoring the means, what if these things had not come to pass? What if immigration from East Asia had been as free and open as immigration from Europe?
Just how many immigrants could we expect to come to America's western shore? What kind of alt-demographics would we have? Would US population in 2010 be more than the OTL ~310,000,000 souls? How much more?
How would a population outflow have effected history in East Asia in the 19th century? Arguably, the 'pressure release valve' of immigration to the Americas kept Europe more stable and less impoverished than would otherwise have been the case. Would a similar effect have been seen in East Asia? Could westernization/modernization have been easier to accomplish in China? Would the monarchy have survived?
East Asian history in the 19th century is one of my particular weak-spots. I know the broad narrative, but any of the specifics are as unknown to me as the history of Alpha Centauri between the 110th century BC and the modern day. Those with better knowledge (here's looking at you Hendryk), I invite you to come help me answer these questions.