If your minor child wants to move out and you approve of this, then your child may file a petition to remove the disabilities of minority under Texas Family Code section 31.001 et seq. in your local family district court or other appropriate court. This petition must be verified by a parent, but not necessarily both parents. The petition to remove the disabilities of minority must also provide 1) the name, age, and place of residence of the child, 2) the name and place of residence of each living parent, 3) the name and place of residence of the guardian of the person and the guardian of the estate, if any, 4) the name and place of residence of the managing conservator, if any, 5) the reasons why removal would be in the best interest of the minor, and 6) the purposes for which removal is requested. The court will then appoint an attorney to represent your child. If the court determines that emancipation is in the best interests of your child, then the court will order him emancipated. At this point, your child is considered an adult, and you're no longer legally liable for your child's decisions.
If your child under 17 moves out without your permission (runs away), this would be considered a status offense. The police could forcefully return your child to your home. After multiple incidents, your child could be considered a habitual runaway, and the state might get involved. Adults in Texas who allow a runaway child to live with them face charges of harboring a runaway under the Texas Penal Code among other charges.