carrying capacity
Actually, I can't sponsor ANY number. There's a quota. Every one I sponsor is one less who gets in by other means. Maybe I get to choose WHO gets in, but I don't get to choose how many.
As for carrying capacity, it depends how we end up living.
If by European standards, I would reckon about 60-100 million vs 20 million now. It means we have to drink other people's bathwater (cleaned up, of course).
By Asian standards, I reckon half to one billion, but it wouldn't be a whole lot of fun.
OTOH, living in Asia and Central or South America in 50-100 years isn't going to be a whole lot of fun unless the population growth stabilises PDQ.