Uncontested divorce refers to a divorce in which parties have been able to reach an agreement on their own or have relatively few issues that are not agreed upon. Whether a divorce is contested or uncontested does not affect the way a divorce is filed or the process for finalizing the case.
While most people use the terms "full custody" or "equal custody", those are not actual legal terms in Texas. There is a presumption that all separated parents shall be named Joint Managing Conservators which means they share equal rights and duties to their children.
Final Orders regarding your children can be modified or changed under certain circumstances. Generally, a custody order can be modified if there has been a material and substantial change in circumstance since the previous order was entered.