After escaping the Imperial Dalek mothership, (TV: Remembrance of the Daleks) Davros eventually found a new home in a Dalek command ship he called his own.
History
Exiled from the Dalek Empire before the outbreak of the Last Great Time War, Davros lived in his command ship, attended to by genetically engineered servants and experimenting on discarded casings. When the Empire recruited Davros, the command ship invaded Gryphon's Reach only to be defeated by the Eleventh Doctor. Exiled for his failure, Davros took his ship to Alacracis IV in an attempt to trap the Doctor only to be outsmarted. Returning to his craft, Davros pondered abandoning the Daleks before they asked for his help in the Time War. (PROSE: Father of the Daleks)
The command ship was destroyed in the "very first year" of the Time War when it flew into the jaws of the Nightmare Child. It had been believed by all at the time that Davros was killed in this incident. However, Dalek Caan, a survivor of the Time War and the Cult of Skaro, used a temporal shift to break the time-lock and save Davros from the doomed vessel. Following this, Davros would go on to found the New Dalek Empire. (TV: The Stolen Earth)