it's not up until 21 in NY?
It depends on the circumstances. If the parents outright kick their child out of the house, support is required. If the child leaves on his or her own without permission or without good cause, the parents aren't responsible. Furthermore, if the child refuses to obey reasonable parental rules, he or she forfeits the right to be supported.
More often than not, the child has to take his or her parents to court to obtain support, though.