There are various types of custody arrangements, including joint custody, sole custody, legal custody, physical custody and shared custody. When opting to change from joint custody to sole custody you must prove in court that this arrangement is beneficial to your child's physical and mental well-being whereas joint custody is not.
Decide what type of custody you want although there is no guarantee this is what the court will award. You could ask for legal sole custody but also share physical custody with your former partner. You may want full legal and sole custody. Or you could have sole legal custody with the other parent involved in decisions pertaining to the child. Your decision should be based on how much involvement you want from your former partner regarding your child.
Hire an attorney and file an action in the court where the custody hearing was previously heard. If there is a standing court order, file a motion to modify that order. Documents will be prepared by your attorney with your help and will include the information that is needed in a change of custody motion. This is not a do-it-yourself action. There is no change of custody form that you can pick up, fill out and file with the court on your own.
Understand beforehand that courts do not tend to award sole legal and physical custody to a parent unless the court believes the other parent is unfit. It is incumbent upon you to prove that the other parent shouldn't have access to the child. Even when the other parent is considered unfit, he or she is sometimes granted supervised visitation rights.
Prepare to show evidence when going into court to get the custodial arrangement changed from joint to sole custody. You must back up your claims that joint custody is not in the child's best interest by showing concrete evidence. Bring witnesses who have observed the interactions between your former partner and the child and which indicate that the parent is unfit. The determination is going to be made by the court based on what is the best interest of the child and not what is the best interest of the parent. You must prove that time spent with the other parent has an adverse effect on your child. You must be able to prove that you provide a safe environment for your child and are the better parent.