Can you make the father sign over his parental rights even though there are no court documents?
No, only the court can permanently terminate parental rights.
Courts are very reluctant to take away all parental rights except
in extreme circumstances of neglect and/or abuse. After
establishing paternity, a biological father has the legal right to
seek custody or visitation privileges. He will also be held legally
obligated to pay child support, provide adequate medical care and
such other issues so ordered by the court.