what is the form called/possible to loose parental rights by refusing to sign bc

Hello again...I would like to know if anyone might know the specific name of the form I can use to get custody, visitation and child support "legal" so to speak.

Dad and I were never married, the child is 9 years old. Dad was in and out of jail and never had much contact with our daughter (although I have always made my address and phone number available to him.) I never asked for child support.

He is trying to turn his life around (so he says) and wants to have a relationship with our daughter. I found out recently from this board that neither one of us legal has custody of her and custody isn't implied even though she has lived with me all her life.

I don't think he will pull anything, but you never know. I want to file for sole custody and reasonable supervised visitation (the times he has seen her recently have been supervised...at a mutual friend's house, due to dad's police record, I won't let him pick her up otherwise) and minimal child support. There is a site from the state of FL supreme court where you can download the forms, but I don't know the name of the form.

Also, just a thought...dad never signed child's birth certificate and flatly refuses to do so but doesn't contest that our daughter is his. If he insists on not signing it, is there a way I can petition the court to give him x amount of days to do so, if not, could he loose his parental rights, opening the door for my husband to adopt our daughter? I would never deny her contact with bio dad if she wants to have a relationship with him, adoption or not...but she hardly knows him and his track record isn't good as far as "turning his life around" and my husband has been "daddy" for 5 years. One judge already allowed her name to be changed to my married name, even though dad contested it.