Can I terminate my children’s father’s rights if he hasn’t seenthem in over 2 years?

The State of Texas does have provisions for terminating the parental rights of parents for certain acts or omissions.  The situation described in your question would fall into the omission category.  If the father of your children has not seen them in over 2 years and has failed to provide for support them for at least of a period of one year within his ability, then you would have a basis of filing for an involuntary termination of his parental rights.  If he has not seen the children, but has continued to support them, then involuntary termination will be a bit more difficult.  Voluntary termination is also an option.  If he isn't interested in being a dad and does not want the obligation of paying child support, he may agree to a voluntary termination.  Regardless of whether you are seeking an involuntary or voluntary termination, you will have to show the court that the termination is in the best interest of the children.  Courts are sometimes reluctant to terminate a father's role, when there is not a new dad in the picture to pick up those usual responsibilities.   This isn't necessarily controlling, but it is a factor they will consider.  Before you file for a termination, you also want to consider the long-term consequences for your children.  It is extremely frustrating when one parent is not contributing.  But if the father should die, and the children's rights have been terminated, then the termination could affect their right to certain benefits or inheritance rights.  Consulting with a family law attorney can help you sort through all of the factors in favor of and against termination and  the advantages and disadvantages for your children.