In my experience, most judges will not allow you to relinquish your parental rights including an obligation to pay child support unless there is another willing person such as a step parent willing to take on the responsibility. It is difficult to be relieved of a child support obligation because the right belongs to the child rather than the parents. If circumstances change, the child may later need support and a claim could be made. The claim by your ex that he will not claim support from you probably will not be legally binding if he changes his mind.
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