Many people confuse these terms. While many people use the term "custody" loosely to describe the arrangement between former spouses and their kids, the Texas Family Code and family lawyers and judges do not use this term.
"Possession" simply means the right to have the child with you. "Conservatorship" means all of the rights and duties of both parents regarding a child, such as determining where the child lives, receiving or paying child support, making decisions or giving consent for the child regarding marriage, joining the military, medical issues and educational issues.
Unless you convince the court or the other parent to do something different, "joint managing conservatorship" is presumed to be in the best interest of the child in most cases. All the rights regarding your child will be laid out, and either you and your spouse will have to agree on how to divide up or share each of these rights, or the court will decide for you.
Many of the rights can be shared, such as the right to take the child for medical treatment when they are injured or ill while in your possession, or the right to attend school and extracurricular activities. Other rights have various options, such as the right to consent to your child joining the military when they turn 17 years old. In this example, you could agree that either party can consent, or you can require that both parties must consent in order for it to happen.
A right not shared is the right to designate the primary residence of the child. This will be the address the child gives to his school and also determines their school district. Courts will sometimes refer to this party as the "primary" conservator. If there is a fight regarding children in a Texas divorce, it is often regarding whom should be the primary conservator with this residency right.
Texas law does not favor the mother over the father, or vice-versa, as to who should be the "primary" conservator. However, all things being equal (both mom and dad are good parents with no serious substance abuse, child neglect or psychological issues) Texas courts seem to name the mother as the primary more often than the father, especially if the child is very young.
The primary conservator also has the right to receive child support, regardless of the possession schedule. Child support and possession are completely separate issues, both at the time of the divorce and for the remainder of the time your child is a minor. You cannot stop paying your court-ordered child support simply because the other party denies you your court-ordered possession time, and you cannot deny possession time due to failure to pay child support. If a problem arises, the remedy is to ask the court to enforce the orders. You can agree to no child support being paid by either party if you wish, and spell that out in your agreed order.
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