I can tell you from experience, most judges around here (NC) do not like to grant joint custody, they especially do not like to grant joint physical they prefer to do sole custody with a visitation plan, they feel that is more stable for children than 2 bickering parents and bouncing from one house to another during the week. That's how they see it. Mediation is usually the first step to a custody battle, unless you can get it waived. If you can't reach an agreement at mediation, then a judge will decide. Be aware though, many NC judges are biased concerning women and women usually are the ones that get custody. Unless she had an affair, by law they will take that into consideration when determining custody. They also take into consideration who can best provide for the child, the type of relationship, who did most of the caretaking for the child and who would best encourage a relationship with the other parent, among other things.
Edited to add... (I know it says joint can be granted, but many judges don't care to do this.)
§ 50‑13.2. Who entitled to custody; terms of custody; visitation rights of grandparents; taking child out of State.
(a) An order for custody of a minor child entered pursuant to this section shall award the custody of such child to such person, agency, organization or institution as will best promote the interest and welfare of the child. In making the determination, the court shall consider all relevant factors including acts of domestic violence between the parties, the safety of the child, and the safety of either party from domestic violence by the other party and shall make findings accordingly. An order for custody must include findings of fact which support the determination of what is in the best interest of the child. Between the mother and father, whether natural or adoptive, no presumption shall apply as to who will better promote the interest and welfare of the child. Joint custody to the parents shall be considered upon the request of either parent.
(b) An order for custody of a minor child may grant joint custody to the parents, exclusive custody to one person, agency, organization, or institution, or grant custody to two or more persons, agencies, organizations, or institutions. Any order for custody shall include such terms, including visitation, as will best promote the interest and welfare of the child. If the court finds that domestic violence has occurred, the court shall enter such orders that best protect the children and party who were the victims of domestic violence, in accordance with the provisions of G.S. 50B‑3(a1)(1), (2), and (3). If a party is absent or relocates with or without the children because of an act of domestic violence, the absence or relocation shall not be a factor that weighs against the party in determining custody or visitation. Absent an order of the court to the contrary, each parent shall have equal access to the records of the minor child involving the health, education, and welfare of the child.
(b1) An order for custody of a minor child may provide visitation rights for any grandparent of the child as the court, in its discretion, deems appropriate. As used in this subsection, "grandparent" includes a biological grandparent of a child adopted by a stepparent or a relative of the child where a substantial relationship exists between the grandparent and the child. Under no circumstances shall a biological grandparent of a child adopted by adoptive parents, neither of whom is related to the child and where parental rights of both biological parents have been terminated, be entitled to visitation rights.
(c) An order for custody of a minor child may provide for such child to be taken outside of the State, but if the order contemplates the return of the child to this State, the judge may require the person, agency, organization or institution having custody out of this State to give bond or other security conditioned upon the return of the child to this State in accordance with the order of the court.
(d) If, within a reasonable time, one parent fails to consent to adoption pursuant to Chapter 48 of the General Statutes or parental rights have not been terminated, the consent of the other consenting parent shall not be effective in an action for custody of the child. (1957, c. 545; 1967, c. 1153, s. 2; 1977, c. 501, s. 2; 1979, c. 967; 1981, c. 735, ss. 1, 2; 1985, c. 575, s. 3; 1987, c. 541, s. 2; c. 776; 1995 (Reg. Sess., 1996), c. 591, s. 5; 2004‑186, s. 17.1.)