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Kentucky’s Supreme Court is being asked to decide what it means to be a parent in today’s ever-changing definition of family.

Two women — former partners identified in court only by their initials — are fighting over custody of a 9-year-old girl.

One woman had a baby with the help of a sperm donor in 2006, but the women’s relationship ended in 2011. Now, the biological mother has cut off contact with the other woman and married a man. That man is trying to adopt the girl. The other woman wants to block the adoption, and she won a favorable family court ruling.

An appeals court reversed that ruling. The Kentucky Supreme Court will hear arguments in the case Thursday.

It’s one of several such disputes across the country.