Not unless there's someone else willing to adopt your child. Texas courts don't like terminating parent-child relationships without someone else willing to support the child as a parent. If your husband wants to adopt your 12 year old son, that'd be a likely scenario where a court would terminate your ex-husband's relationship. However, if that's not the case, a court would be hard-pressed to terminate just because he doesn't want to pay child support.
He can sign a voluntary relinquishment. As repulsive as that is, a judge may still decide not to terminate. The judge may not believe it is in the best interest of the child to terminate. If your current husband wants to adopt you may have a much more assured outcome. You need a lawyer.
This answer does not create an attorney-client relationship. This information is general to anyone, and is not intended to be advice to anyone's specific situation. You should consult an attorney immediately concerning your legal issue. This is not intended to be relied upon as a final or conclusive solution.
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