I've been married for a year now, I'm trying to adopt my stepchildren. In my case the father does not have any legal paper to work or live in the United states, he's never given them anything up to support them ever since I've been with my wife. I want to know if the court is going to waiver his right to them, because he's never been there for them?

Your state will have very specific rules. Normally there will have to be an attempt to contact the father, if he will not show up in court, often the court will allow the adoption.