Legal Question in Family Law in California

It could be either parent or both (one in each direction). Check your custody agreement. If its not been ordered by the court, you can move to have the custody order amended. You will not have to pay for an additional filing, but you will have to perform mediation, where you will more than likely resolve it. Given that, it is far more efficient and less hassle for you and your child's other parent to simply attempt to discuss it yourselves. Otherwise, the court which originally granted a custody order (if one exists), retains jurisdiction regardless of your having moved.

There is no official rule. Either you work it out or a court decides what is fair. If you have both moved out of state, you might also consider moving the case to the state where the child resides.