My name was not on the title, but in our state all assets and debts acquired during a marriage are shared (there are a few exceptions in the property laws but the lawyers assured me I was entitled to half the house if I wanted to fight for it).
The rest of it is complicated, but I gave up my claim to everything. You're right, custody and support are separate. There is no custody agreement and no support order. The reason there is no order is because he has legally abandoned his kids at this point. I can file for the abandonment but a judge will still give him a chance to have custody or visitation of the kids if he says he wants it and I don't want to do anything to provoke that. I know that seems crazy, and it makes me uncomfortable to not have an official order, but one of the attorneys I consulted deals with abuse cases and she advised me not to fight him if I don't need the money.
It's hard to explain this to people because they never understand but you have to trust me that my ex-husband is not the kind of man that you want to fight. I have very little documentation about the years of abuse, just a couple of text messages and emails where I was able to provoke him into admitting some stuff after we separated, but even that is shaky. And I never filed for a PFA in all the years of marriage and even after some incidents after we separated, so doing so now when there has been no contact for so long would look bad. The abuse lawyer told me this. Two lawyers looked at what I had and told me I didn't have a good case, that there was no good outcome when you consider the circumstances, especially the fact that fighting him for money leaves my kids vulnerable if I end up with the wrong judge. I don't make much, my income is under $30,000/year including the SSI money that I receive for my son who has special needs. I'm not comfortable saying any more than that, but I'm over the income limit for free legal help in my state. The price I was quoted for reduced price legal help was $70/hour, which adds up quick! So I retained a lawyer on my own to file for a quick (cheap) divorce, but she warned me that doing so means I give up all my rights to marital assets. He got everything, the house and most of it's contents, vehicles, retirement accounts, etc. and I've accepted that because every day that the kids and I are free we win, as far as I'm concerned. At this point I'm not worried about the money, I've already given it up, I'm just worried about provoking him. I had accepted that I was going to have to pay off the line of credit, I truly don't care about it because it's just money. I don't want to face what will happen if he is angry about having to pay off the line of credit and I don't really understand how the payoff works.