I'm currently in a relationship with a man who adores my daughter. Her father is absent, and he (my current mate) is looking to legally adopt her. His name isn't on the birth certificate, and he doesn't come around to visit her anymore. The only communication my dauther has with her "father" is through text messages, and that only happens once or twice a year. If the adoption should occur, will her biological father have to sign over his rights, even if he's non-existent in person and on paper?
Is your current mate also your husband? If he is, then you are looking at performing a step-parent adoption.
You do need to tell the court if there is an alleged or legal father of the child. And, the court will need to terminate the rights of the biological father before any adoption can go forward. If biodad has made no attempts to communicate with the child or support the child over the past year, you can ask the court to terminate the alleged father's parental rights on the basis of abandonment. Current case and statutory law holds that "token" or extremely minimal communication does not mean the court cannot terminate rights for abandonment. One text every six months or so certainly seems to me to be a "token" attempt to communicate with his child.
You should consult with an attorney who can further discuss the facts of this case with you and with your current mate. Any adoption will require a background investigation by the state, and you have to pay for it. You want to be sure you can meet that expense, and explore the longterm legal and financial ramifications of such a move - before you do it.