North Carolina petition of partition (forced sale)?

In North Carolina if you file for a petition of partition (forced sale) and two people are on the deed and mortgage unmarried but have a child. While it s going through Court does the person filing for the petition have to live there. I ve heard it takes months maybe years. But this couple hates each other but doesn t want to start a custody battle if one moves out because that can be "abandonment"
The female in this situation wand to keep the house and wants to buy the male out of 5 thousand dollars when she
Did not pay the mortgage for 6 months. There is 15,000 dollars of equity in the house also and 5 grand was put in by the male for renovations.

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