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When you say "disinherit" do you mean can the parent ensure that the child doesn't take anything from the parent's estate if they pass away?
Or are you referring to a situation where the parent gives up their legal rights to the child?
If the father wants to make sure that the children don't inherit, then he just needs to ensure that he has a will in place setting out his specific directives as to who he wants to inherit his estate. If he has a trust, then any assets in the trust would descend according to the trust terms.
The child would be entitled to come after the estate for any child support arrearages, and after that the child would then be entitled to Social Security Survivor benefits. Texas family law provides that future child support payments survive the death of the person who has to pay (“obligor”). So the custodial parent could petition the probate court for continuing child support payments.
So if the parent left the child out out their will intentionally and also out of any trust, then they wouldn't stand to inherit from their estate at all but the estate could still be liable for future child support payments.