Is Solthsteim part of Morrowind or Skyrim?

According to both DLCs in Morrowind and Skyrim, you visit Solthsteim. In Morrowind the island looks like part of Skyrim because of its snowy biomes and trees. In Skyrim it looks like part of Morrowind, those structures and the ashy land, which is what I don't like about that island in the Skyrim game. So, is Solthsteim part of the Morrowind province or the Skyrim province?

Solution 1:

It was part of Skyrim until the Fourth Era, at which point it was gifted to Morrowind in the year 16.

The UESP wiki further notes that this was due to "compassion for the suffering Dunmer people" after the eruption of Red Mountain.