‘Custody’ as a legal expression went out when the Children Act came into force in 1991.  Since then, what the court orders (if it orders anything at all) is simply who the child is to live with – a residence order.

Since 1991 ‘access’ to a child has been ‘contact’ with a child.  You still occasionally see the expression ‘contact to’ a child, originating presumably when lawyers dutifully used the new term ‘contact‘ but failed to make the necessary grammatical adjustment from ‘to to ‘with’.