If you have custody papers, the Court Orders decide the answer to your question. You need to read them. In Texas, there is a presumption in favor of a geographical restriction, so it is highly likely you cannot move without his permission or the permission of the court. However, you have to read your custody papers to determine the answer at this time. Finally, please note, the Court can restrict the children's residence, not yours. You are free to move, even if there is a geographic restriction, but you cannot take the kids with you.
Answer Applies to: Texas
The answer to your question is or should be answered in the court order establishing the custody/parenting responsibilities rules. If it isn't, you probably need to get permission from the court.
Answer Applies to: Colorado
You state that you are the "custodial parent." Does this mean that you have entered a parenting plan? If you have, then, the Washington relocation act will apply. This act puts limits on your ability to move with the children. It also lays out a procedure that you are supposed to follow if you want to move. As a practical matter, what this means is that you are probably either going to have to get the father's permission or follow the relocation act procedure to get the court's permission.
Answer Applies to: Washington
If you currently have joint custody over the children, with specified days and times that the father has to spend time with the child, and moving out of state will make it impossible for him to be able to continue to see the child on these dates and times, then you would be in violation of the current child custody agreement by moving out of state. The best course of action you have is to apply in Family Court for either full custody or to modify the agreement so that you will be able to move out of state without violating the agreement.
Answer Applies to: New York
Depends what your court papers/orders say. Usually you are required to give notice to him and the court, if he objects to the court the court will schedule something. If he doesn't respond, you are free to go. If you go without following the court order, the court can hold you in contempt and require the return of the child (though the return of the child is rare, it does happen).
Answer Applies to: Wisconsin
If you have joint custody (now called shared parenting in Ohio), you are both custodial parents. You will have to see if your plan prohibits you moving out of state without his permission or a court order. Most plans require that. If not, you still have to notify him you are moving, and he could then file for custody due to that.
Answer Applies to: Ohio
If joint custody was established by a court order, you may be violating the order my moving out of state without his permission. If the move interferes with his ability to exercise his visitation, he may be able to file contempt charges against you. You will need to review your court order to determine what you can and cannot do.
Answer Applies to: Georgia
No, you must provide him 30 days written notice by registered mail. If he files an objection in court then the judge will have to decide where the child should live.
Answer Applies to: Kansas
You need either his consent or a court order permitting same.
Answer Applies to: New Jersey
If a court order was entered granting you and the Father timesharing or custody with the child, you cannot move more than 150 miles from the Father without his agreement or a court order authorizing the move. Violating this law can get you into trouble, so you should consult with an attorney in your area regarding the move you are considering and the possible outcomes.
Answer Applies to: Wisconsin