In NJ, do unwed mothers have full custody right from birth? Even with the father having signed the birth certificate? My son's father has been MIA for months and has given his son NO money. The day before the 4th of July, he called and said he wanted to take his son. I said no and it turned into a major fight. As far as I know, he doesn't have a place to live. I filed for custody shortly after and am still waiting for a court date. Should I withdraw? I'm a risking giving him rights by going to court?