The Courts and child advocacy groups support the right of any child to have a relationship with each of his/her parents, regardless how much the parents despise one another. Unless a parent is proven to be abusive and/or incompetent, joint custody is quite common and considered best for the child. Parents are expected to act like grown-ups.
Most states standards are the same in that they look to the "best interest of the child. " Sometimes this is even contrary to what an older child may want. Both parents have an obligation to co-parent the child to the best of their ability.
None, because there is no such custody type, join meaning to bring together, not place in a singular situation, ie one person accepts responsibility, or two separate persons accept different responsibilities. Joint custody?