If you are married, it's possible, certainly more so than if you are unmarried. Generally, courts terminate for criminal reasons or for abandonment (non payment of child support and non involvement in the child's life). Here you don't state any criminal history, and he hasn't abandoned her in the eyes of the state because he continues to pay support.
If you are unmarried, the likelihood of a Judge terminating his rights is very small, absent criminal issues or non-support.
If you are married and your husband now is willing to adopt your daughter, then the father may voluntarily give up his rights to your husband and allow your husband to adopt her. If he does not agree, then it will be at the Judge's discretion to allow the adoption.
I practice in Tarrant, Dallas, Denton, Parker and Wise counties.
I am licensed only in Texas. Answers are based on current Texas law. This is for educational purposes only. This answer is given based on the facts provided above.
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If he pays support, why would you want to terminate his rights? You could limit his rights and still collect support. If you have a spouse who has an established relationship with your child and wants to adopt and support your child, then I would say it's fairly easy to terminate the father's rights. I wouldn't terminate for the sole reason he doesn't see the child. Consult with an aggressive and experienced family law attorney to discuss your options.
I agree with the attorneys that have already answered this question. You need to meet with an attorney in your county and discuss your particular set of facts. It is impossible to give you an answer based on the limited facts you have presented. If he is paying child support, most courts won't terminate his parental rights.