Florida does not recognize your union. There's no same sex divorce in Florida. You may want to ask this question of Vermont lawyers.
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I'm not sure I understand your question. Florida, as I'm sure you know, does not recognize civil unions in the same sense that Vermont once did before gay marriage became legal there. In fact, outside of a few cities in a Florida, domestic partnership is not legal here, so no formal action for dissolution of domestic partnership exists in Florida courts, though I suppose one could be filed in those counties where the cities have enacted domestic partnership laws (Hillsborough, Dade, and Broward, to my knowledge). You don't appear to be seeking timeshare with the child, which Florida recognizes amongst same-sex couples in certain circumstances, and your property has been split, so what would you like to accomplish?
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