The Darth Star, also called Sith space, was the domain of Darth Statler, as well as the meeting place of the Sith Order. Statler resided there to contact his apprentices about his future plans via hologram.
Behind the scenes
The Darth Star was an idea originally in The LFwD Series, where Darth Daniel lived with his master Darth Ben. LFwD was subsequently cancelled, and Daniel decided that the Darth Star should be reused in the Puppet Saga.