I have a very similar case but I have no idea where he lives nor have I received any money since birth, my children are 6&7 now. Would that qualify as abandonment? And what happens if the court can't find him to sign the papers?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

Second, ANY question on law needs to include your general locale as laws vary by area.

What papers are you talking about? If you are referring to an adoption, the court won't look for him. The court will require that YOU make a good faith effort to find him. You will have to prove to the court that you have tried. Your attorney can tell you what that good faith effort means.

You generally cannot use abandonment, especially not to just get his rights terminated. But you should have an attorney to prepare the adoption petition. Your attorney will advise you.

Yes each state has its own laws ( assuming you are in the US) but merely abandoning the kids is often not a reason to take rights away, ( but could be part of a entire list of other issues)

You will have to meet all of the courts conditions for searching for the bio father ( or fathers)

It will be a longer and a much more costly case when you can't find the father. And you will need an attorney