The correct answer is C) deck load, lower-hull liquids, external loads, and deploying anchors. The lightweight of a vessel, such as the DEEP DRILLER, refers to the condition of the vessel prior to loading any cargo, fuel, water, stores, passengers, or crew. This includes the weight of the hull, machinery, equipment, and any other permanent fixtures. The lightweight does not include the weight of the deck load, lower-hull liquids (e.g., fuel, water, ballast), external loads (e.g., cranes, drilling equipment), or the weight of the anchors and anchor chains. The other options are incorrect because they do not fully encompass all the elements that are excluded from the lightweight condition. Option A includes deck load and lower-hull liquids but omits external loads and anchor deployment. Option B is even more limited, including only deck load and lower-hull liquids. Option D is the most limited, considering only the deck load.