What happens when the natural mother wants these signed?

If you sign over your rights, you are agreeing you are no longer a parent of the child. You should no longer pay child support but you don't get visits either. Its like walking away completely. Full custody means that the child would live with her 100% of the time...how much ability that parent has to make decisions regardin the child on her own can be variable. Visitation can still be allowed and child custody is determined then by the court based on everyone's income and expenses. The drama over you and her probably won't get solved...and all you can do is state the facts to the court if asked...its not worth arguing with her over it. Its probably best you consult a lawyer...even just a one time meeting to understand what is happening.