When a man agrees to be his ex-girlfriend's sperm donor...

... with a physician as intermediary and thereby avoids the obligation of paying child support, should he succeed if, later, he asks a court to require the mother to share custody of the child?

The man is the actor Jason Patric, who says he gave the sperm on condition that the woman not seek child support, at a time when, he says, he didn't have enough money.

I'll add what I'd put on a law school exam: If you need more factual information in order to answer, tell me what it is and why you need it?