I married my husband 9 1/2 years ago and we had 2 children together. We separted in May of 2005 because of his heroin addiction. The children have always been with me and until last summer he had no contact with them ( partially because of a protection order preventing him from contact until 2009). He now lives down the street and the only contact he has had with them is because I practically forced him to do so (they asked to meet their father). He has seen them 3 or 4 times in passing since then but doesn't really acknowledge them. I am wanting to seek a divorce but he does not want one. He argues he will ask for visitation or even custody and I do not want him to have either (unless its supervised). I can't afford a costly battle which is what he claims he will put me in.He receives Disability checks so I receive payments via that for child support so that isn't an issue. Any suggestions?

Retain an Attorney and file for divorce. Ask for supervised visitation and prove that he is somehow a danger to the children. He can ask for anything he wants to ask for. Whether he will "get it" remains to be seen.

This is a pretty standard threat - a parent who has no interest in the child but holds custody/visitation over the head of the other parent as a constant threat.

I wouldn't let him bully me like this.