Dead beat dads, stand up step fathers

Raeleigh
My sons father and I haven't been together in a few years, he is 5 and his dad has been in his life on weekends for the past couple years.. But mainly his father would pick him up and take him to a family members house to stay. He's never had his own place he's always lived with his mother so he could have a babysitter whenever he wanted to leave. He has never paid child support not one dime. This past year he got into drugs bad.. I guess it started 2- 2 1/2 years ago just no one saw it. So this past year I allowed him to still see our son as long as he was around his mom to make sure nothing bad happened. About three months ago he hit absolute bottom and his mother told me to keep our son away because the dad was not in a good place or safe. In the past few months he's called or said he'd call and he'd tell our son he'd see him and never show. Now he's saying he wants to give up his rights... I know it's not like he can just walk into the court house and it happen that quick you have to go to court see a judge ect.
I've been with my fiancé for the past three years. And he has been more of a father to my son than his actual father. He supports him financially, he reads him stories, tucks him in a night, bonds with him spends time with him.. The things that matter...  
My question is has anyone dealt with anything like this and have their fiancé step up and be "dad"  even have their child starts calling them that?