Videogame executive Xu Bo, said to have more than 100 children, and other elites build mega-families, testing citizenship laws and drawing on nannies, IVF and legal firms set up to help them

The market has grown so sophisticated, experts say, that at times Chinese parents have had U.S.-born children without stepping foot in the country. A thriving mini-industry of American surrogacy agencies, law firms, clinics, delivery agencies and nanny services—even to pick up the newborns from hospitals—has risen to accommodate the demand, permitting parents to ship their genetic material abroad and get a baby delivered back, at a cost of up to $200,000 per child.

The growing Asian market for international fertility services has drawn the attention of American investors, including Peter Thiel, whose family office has backed a chain of IVF clinics across Southeast Asia and a recently opened branch in Los Angeles.