The case is Ramey v. Sutton and was just decided by the supreme Court.
In the case, Charlene Ramey and Kimberly Sutton were engaged and in a steady relationship for a term of years. Through a male friend’s donation, Sutton gave birth to a child. Ramey stayed at home with the child and became known as “mom” to the child while Sutton was more often referred to as ”Kim”.
After ten years of co-parenting, the couple split and Sutton, as biological mother, sought to end all interaction between Ramey and their child. Ramey brought suit for parental rights (custody and visitations). The District Court, basing its decision upon the couple never finalizing marriage (not allowed in Oklahoma until the U.S. Supreme Court decision earlier this year), issued a summary judgment in favor of Sutton. Ramey appealed.
In a 9-0 decision, the Supreme Court reversed, finding Ramey had standing to have her issues heard, and the case was remanded to District Court.
So, there will still be questions as to what parental rights will be given a non-spouse, non-biological parent, but the courts appear to want the same consideration given as happens with heterosexual couples.