The term "full" custody is not a legal term. I have no idea what that means.
There is sole managing conservatorship and joint managing conservatorship in the State of Texas.
Chapter 153 of the Texas Family Code covers Conservatorship, Possession & Access.
The Texas Family Code is available on-line for free. Google it. Read it.
Section 153.001 is the Public Policy of the State of Texas
It basically states that children should have frequent and continuing contact with parents who have show the ability to act in the best interest of the child. T encourage parents to share in the rights & duties of raising their child after the parents have separated or dissolved their marriage and children need a safe, stable and nonviolent environment.
Section 153.131- Presumption that parent to be appointed managing conservator
It is a rebuttable presumption that the appointment of the parents of a child as joint managing conservators is in the best interest of the child. A finding a family violence involving the parents of a child removes the presumption under this subsection.
Section 153.07-076 - These sections discuss "rights and duties"
Rights to make decisions are very important regarding the child. Take this list very seriously. Don't allow the other parent to make "all decisions independently". This is where a parent should "fight" for their child. Future decision making regarding the child are vital to parenting a child.