A special case of this question is that the destination of the immigration is the US. Let's assume this, and let's also assume that an immigrant is magically and automatically converted into a proper US citizen (believing in women's rights, having gay buddies, etc.). Now imagine that EVERYONE outside of the US immigrates to the US. Because nobody would be left outside of the US, the US could expand to cover the entire planet. The real question now is: Is the US self-sustainable, i.e. can it function totally on its own?