According to the Texas State Legislature, parental rights can be involuntarily terminated if the parent endangers, abandons or refuses to adequately care for the child. If the parent is convicted of a crime or incarcerated, parental rights can also be terminated. Parental rights can be voluntarily terminated if the child is not genetically the parent's or if the child is put up for adoption within 48 hours of birth.
The Texas State Legislature further notes that parental rights can be voluntarily terminated in extraordinary circumstances, such as if the child is the product of a crime or if the child was born alive after an abortion procedure. The rights of a child's biological father may be revoked if the father knows about the child but is not present during the pregnancy and birth, does not provide financial support to the child or cannot be found.
The Law Office of Janis Alexander Cross notes that parental rights cannot be terminated to avoid paying child support. To terminate parental rights voluntarily, the parent has to relinquish custody of the child to an adoptive parent. In the case of a parent giving the child up for adoption, the child may pass into the custody of the state until a suitable adoptive parent or guardian can be found.