You've fleshed out that scenario rather, Bert. No information that tells you it's a "deadbeat" father. He might have no idea he's the father. She might have no idea whose the father, for that matter.

As for his relationship with his daughter - the only reason he's got any visitation rights is because he is the legal father. Take that away and he'd got no rights at all. He loses his daughter. She loses his father.