This is all speculation however, as there has never been any proof that any such station was ever built. This mobile battlestation, if it ever existed, was apparently named the Tarkin as well making it the 'Tarkin-I Class Star Dreadnought'. There is a persistent rumor that another reason the massive ships were designated the Tarkin-II has something to do with a Palpatine-Era Shadow Project involving a severely cut-down version of the Death Star's Superlaser mated to the aft section of an Executor-Class Command Ship.
This is because the government which contracted with Kuat Drive Yards for the warship's construction delivered plans and work orders for the inclusion of the Gravshock Bombard during the initial construction phases of the Tarkin and rather than simply rename it or issue a new construction contract for it, Kuat Drive Yards, with the consent of the purchasing government, the Keltarrin Protectorate, instead released it as the Tarkin-II Class Star Dreadnought. The Tarkin-II Class Star Dreadnought is most notable, aside from its unprecedented size and firepower, for the fact that there was no Tarkin-I Class Star Dreadnought.