Hello I'm looking to get an answer on what I need to do in order to sign my parental rights over of my children to their mother?

Has her lawyer contacted you because her new husband wants to adopt? If yes, ask him. If no, you cant. Please see the hundreds of other threads or the sticky at the top of the page for more details.

As noted unless the other parent is married and they want to adopt, you can not just sign your rights away,

You can allow the mother to file for full custody legal and physcial, you can agree to no visits but you can't just sign rights away.