If the mother of my children is banned from ever having custody, and I voluntary terminate my custody, but the children are going to a good home where I can visit, do I still have to pay child support?

The only way you would be relieved of paying child support is if the children are legally adopted and you are no longer the legal father.

You are still financially obligated as they are still your children unless a Court deems otherwise in an adoption matter.

What do you mean when you say the mother is " banned " from custody ? She still may retain certain legal rights even without physical custody.