I am engaged to be married to my high school sweetheart, a man I have been best friends with and have known for over 15 years. We have been living together for 3 years now and he has become the REAL father to all four of my children. I was in a VERY abusive relationship for 7 years with my children's biological father. It ended with him in jail and me with several broken bones. He had been neglectful to the kids... apparently when I left for work he would lock them up, and ignore them. They were just babies. He has not seen them in over 5 years, and the only time I have seen him is in child support court. In all these years, support was ordered, but he hasn't paid a dime. He continuously files for disability, so they cannot make him pay... and he somehow obtained custody of one of his other 5 children ( that I didn't know about until after our relationship). His daughter is apparently mentally disabled in some ways, and he now receives government funding to support him and his daughter, while we see nothing. He currently owes my children $30,000 approx, and I don't want another penny added to it. I want to find if there is a way I can get full custody so that my children don't need to go through anymore pain, and my new husband can take his rightful place as their dad. ( which he will be no matter what anyhow) :) thank you.

You did not say where you live, so I can give you a "general" answer. In most places you will need to be married for at least one year.

After that you hire an attorney who will first contact your ex and try to get him to sign over his rights to allow the adoption. If he will, easy and the paper work goes to court and the adoption goes though.

If he will not sign, then of course it starts costing a lot more money since you will have to argue this in court. You file, and your ex is served. If he does not show up, a good chance judge will listen to your argument and you will win.

If he objects and shows up to fight, you have good evidence, police reports of his abuse to you. Reports of his neglect of the kids (** I am assuming all of this is documented)
Then the fact he has not contacted and not paid support. One can not guess what a judge will do but you try and see what happens