Who do I talk to in order to sign off any and all connections with my children?I don't want any connections to them at all,including child support.

You can't. It isn't that easy. You don't get to just "return" them. There are tons of posts here as to why not, look them up yourself. You can just ignore them if you chose, but you will pay child support. The state will not be daddy for you.

Talk to God, since you don't have a pray to get that unless the parent with custody has someone who wants to adopt the child.

You don't have to visit, you don't have to carry their photo, but you will write a child support check or perhaps go to jail or lose your drivers license if you don't. There is no way to get out of child support unless someone is adopting the child.