For me to adopt my 18 year old granddaughter, do her parents have to be notified?
Since your granddaughter is 18, she is legally considered to be an adult in the eyes of the law. In TX, the adoption of an adult is governed by Chapter 162, Subchapter F. Adoption of an Adult.
Section 162.501 provides that the court may grant the petition of an adult residing in the state to adopt another adult. Section 162.503/4, lists the requirements for such an adoption: (1) If the petitioner is married, both spouses must join in the petition for adoption; and (2) a court may not grant an adoption unless the adult consents in writing to be adopted by the petitioner.
So it does not appear that an adult biological parents must consent to the adoption. Since this can all get tricky, you should consult directly with a family law attorney on your area.