Legal custody means having the legal responsibility for caring for a child. The divorce judgment or court order will usually say who gets custody. Either parent (or both) can get custody.
If the parents agree between themselves on custody, they can avoid a long and expensive court case. But if they can't agree, the judge will hear both sides and decide what is in the best interests of the child, not the parents. The judge will consider many factors, such as:
Emotional ties of the children to parents and other family;
Attitude of the parents' towards the child;
Whether one parent has abused the other;
If one parent will help the other parent keep close ties with the child;
Any criminal record of either of the parents;
The parents' emotional stability;
Home environment;
The child's age, sex, and health; and
The child's preference (if old enough).
Judges will often award permanent legal custody to the parent who has had physical custody of the child prior to the court hearing (this is known as "maintaining the status quo."). Judges do not like to change the living situation of a child who is doing well.