California’s highest court was asked Tuesday to create a legal framework for what constitutes a family as justices weighed parental rights for lesbian couples who broke up after having children.

The state Supreme Court, hearing oral arguments in the cases of three women seeking child custody or support from their former partners, pondered whether children from same-sex households should be treated the same under the law as out-of-wedlock offspring of heterosexuals.

Attorneys for some of the women and the California attorney general argued that children should be given the same protections they would have with two traditional parents, since gays cannot marry and may have legitimate reasons for not registering as domestic partners or formally adopting their children.

They urged the court to apply long-standing laws governing absent fathers to estranged gay and lesbian couples who used reproductive science to conceive, a practice that leaves one partner without a genetic link to the family.