China *does* have an immigration problem, but it's INTERNAL to the country. China's "residency" system means you are supposed to stay at where you're born and only move upon approval. In practice, people go where the jobs are, leaving mostly the elderly and children in the outlying villages, while they head into the cities for jobs. In the recent years some of the middle-aged moved back to the villages, after finding themselves unable to compete with the youngsters for jobs in high-tech fields (such as the Foxconn factories in Shenzhen that makes your iPods and iPhones). If you can't prove residency, you won't get hospital care, school, or even right to have children.
So China *does* have an illegal immigration problem, but it's one that guailo (i.e. gaijin) do not see.