Texas law-
If a biological father is not cooperative with the birth mother in her adoption plan, or if the identity or whereabouts of the biological father are unknown, his rights may be terminated without notice by use of the Texas Paternity Registry. Texas law requires a biological father to register with the Texas Paternity Registry within 31 days of the birth of the child.
If the biological father fails to register, the Court may terminate the rights of the biological father due to his failure to register as required by state law.
After parental rights have been terminated, the agency is appointed as managing conservator of the child. The prospective adoptive parents will be able to finalize their adoption after the child has resided in their home for 6 months. During this six-month time frame, the agency is responsible for supervision of the placement as required by Texas licensing standards. After these supervision requirements have been met, and the six months has elapsed, the agency will provide written consent (as managing conservators) to the adoption. A court hearing in the court of continuing jurisdiction is necessary to grant the adoption.
http://www.adoptionaccess.com/texas_laws.htm
This entire procedure is initiated in court and approved by a judge. Not after 6 months but from the beginning. You do not just take a child home for 6 months then contact the courts.