Custody cases involving same-sex couples

In recent years, there has been a rise in the number of same-sex couples with children. Like heterosexual couples with children, when same-sex couples with children split (whether they are married or not), there may be a dispute over the custody of the children. What are some of the issues that may arise in custody cases involving same-sex couples? How are those issues similar and/or different from the issues that arise in custody cases involving heterosexual parents? How does the Family Court currently address these issues? How should these issues be addressed?