This task given by Lord Arthur to build the warship is merely an assessment; he just wants to check if various workshops still have the ability to cast a legendary battleship. As for the ownership of the crafted legendary battleship, he doesn't care; each workshop can decide for themselves.
Generally speaking, the ownership of such jointly manufactured final products belongs to the host, which means the party providing the venue, equipment, and materials. Others will just contribute labor and ultimately have their names included in the list of the warship's makers.
After all, it's not a business collaboration but an assessment task; participants will succeed as long as they pass the assessment.
