K9 Mark IV was a recreation and enhancement of the Mark III created by the Tenth Doctor as a second present for Sarah Jane. (TV: School Reunion) This model continued in service to his mistress, Luke Smith, Clyde Langer, and Rani Chandra and was known by Maria Jackson and Kelsey Hooper. He was left fixing a black hole in Sweden for many years, but after returning to Earth, was used sparingly, until he went to university with Luke Smith. (TV: The Nightmare Man)
With his great intelligence, he had a tendency to bore people with facts and did not stop immediately when asked, as he did to Leela on Pluto. When being told that he would have to stay behind in the TARDIS, K9 often argued, giving the Doctor reasons why he should go such as "he would be a good dog." K9 always wanted to assist the Doctor. He had great intelligence and skill at chess, claiming to be able to beat the Doctor in six moves (although this may only have been because he was programmed with all chess games since 1886). (TV: The Sun Makers, The Androids of Tara) K9 had an aggression mode. (TV: State of Decay)
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K9 had a personality very consistent across the models with some contact with the Doctor. He was polite and formal, with pedantry bordering on condescension. Though he often displayed feelings such as sorrow (TV: The Invasion of Time) and self-regard (TV: School Reunion), he often stated that he had not been programmed to have emotions. (TV: Invasion of the Bane)
Introduced into the plot in The Invasion of Time, K9 Mark II first actually appear on-screen in The Ribos Operation (1978). More mobile than his predecessor, Mark II exhibited the ability to sense and warn others of danger. He travels as a companion alongside the Doctor and Romana. Around the time of Romana's regeneration (the transition from actress Mary Tamm to Lalla Ward), the K9 character was explained as suffering from "laryngitis" to accommodate Leeson's departure from the series at the start of the 1979–80 season; for this time, he was portrayed by David Brierley, until Leeson's return for the 1980–81 season. When the Doctor and Romana travel to the parallel universe of E-Space, K9 is severely damaged, in Warriors' Gate (1981). The damage was such that K9 could only function in E-Space; when Romana decided to stay and forge her own path, the Doctor gave K9 to her. The character makes subsequent appearances in remakes of the unfinished serial Shada, alongside the Eighth Doctor (Paul McGann); the 2003 Shada audio play and webcast depict K9 Mark II as having returned to Gallifrey with Romana, now Lady President of the Time Lords, where the Doctor visits them. It is not clear if either of these audio appearances are considered canonical in relation to the continuity of the TV series.
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