My daughter and her husband divorced in Nov. he left here and the 2 children to live with another woman in Aug. He has now moved from Ark. To TX and says that he can't pay $105.00 a week for support and she suggested that he sign his rights away and he wants to, so how do they do that with a judgement for child support in effect?

My daughter and her husband divorced in Nov. he left here and the 2 children to live with another woman in Aug. He has now moved from Ark. to TX and says that he can't pay $105.00 a week for support and she suggested that he sign his rights away and he wants to, so how do they do that with a judgement for child support in effect??

There is a Sticky at the top of the Family Law thread which outlines termination of parental rights:
https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

If there is not another party willing to adopt the children, then odds are the courts will not allow him to relinquish his rights.

Your daughter's options are to agree to accept a lesser amount of child support from him, or to stay with the current agreement. If he does not pay, the state will go after him in numerous ways: suspending his driver's license, intercepting his tax return, contacting his employer to have them withhold, and ultimately, issuing a warrant for failure to pay support.