The Flagship Mark II, named due to its status as the successor to the original Flagship and usually simply called "Mark II", is a Precursor vessel discovered by The Captain of the original Flagship some time after the events of Star Control II, possibly on a factory world similar to Unzervalt.
Unlike the first Precursor vessel utilized by the Alliance, this one was a much larger, more powerful vehicle, compared to a "cruiser"-class vessel as opposed to the Flagship Mark I's "shuttle" or "tug". It has a large ellipsoid or "saucer-shaped" configuration, matching the Slylandro's descriptions of the ships that made up the bulk of the Precursor fleet used to flee to the Galactic Core.
Few details have yet been released about the famous Captain's adventures on the Mark II. Though many thought his heroic role in destroying the Sa-Matra and ending Ur-Quan threat might lead him to an early retirement to raise a family with his lover Talana, his discovery of the Mark II led him on a strange, mysterious set of travels about which much speculation abounds, but which are assumed to have been as important to his own destiny and the galaxy's as his adventures on the Mark I were. It was not until he returned victorious from these secret journeys, his tasks finished, that he and Talana were free to exchange marital vows and raise their children, though the Mark II itself was to remain in service long into his old age.