The correct answer is C) center of flotation. A MODU (Mobile Offshore Drilling Unit) lists and trims about its center of flotation, which is the point in the waterplane where the buoyant forces act. This is the point where the ship's displacement is balanced, and any changes in the distribution of weight or buoyancy will cause the MODU to list or trim around this point. The other options are incorrect because the centroid of the underwater volume (A) and the center of buoyancy (B) are not the points about which a MODU lists and trims, while the center of gravity (D) is the point about which a ship rotates, but not the specific point for listing and trimming.