Vessel is held in an international business corporation that is in the British Virgin Islands. The vessel itself has a year long crusing permit with the US Coast guard and is docked most of the year on the S. C. coast. Does the SC citizen that owns shares in the BVI corporation have to pay SC property tax?

Thist type of question requires detailed research into South Carolina tax law and really is NOT the type of question appropriate for this type of forum.

You need to consult with a tax professional who practices in South Carolina, and expect to pay him/her for their time and effort.