In one of the infinite parallel universes of "possible space", (COMIC: Fire and Brimstone) the Master was the grandson and heir of Barusa. He was believed to be Barusa's only living descendant, but Barusa actually had another grandson, the Master's greatest rival and — secretly — his half-brother: the Doctor. (PROSE: The Chronicles of Doctor Who?)
Ulysses's only legitimate son became known as the Master "in later lives". By the time his contemporary the Doctor was in his eighth incarnation, the Master was highly influential on Gallifrey, promoting an ideology according to which the Time Lords should endeavour to conquer their galaxy and rule it directly by force. He wished, and expected, to become President upon Barusa's final regeneration, upon which a Time Lord would lose their physical form and thus have to pass on any offices they held in the physical world. However, when Barusa felt his final regeneration approaching, he instead put forward the Doctor as his successor, to the Master's outrage. The Master turned public opinion and against the Doctor and, while Barusa was on his deathbed, the Doctor was exiled from the Domed City.
There, he did not die as the Master hoped but, after wandering for months, nearing death, he was found by the Outcasts, a secret sect who guarded the secrets of the Tomb of Rassilon. With their help, the Doctor found the Scrolls of Rassilon and brought them back to the Domed City where he found Barusa on his deathbed. Barusa revealed to him that he was Ulysses's son by a human mother before passing away. As the Presidency transferred to him, the Master ordered the Doctor executed and the Doctor had to flee, stealing a TARDIS. The instant of his leaving Gallifrey coincided with Barusa's final regeneration, during which his soul left his body. However, instead of taking root in the crystals of the Domed City, Barusa's spirit somehow found itself drawn to the Doctor's TARDIS, merging with it and becoming the Doctor's first and constant companion on his flight through time and space.
Eventually, the Doctor's TARDIS was drawn off-course and back to Gallifrey, where the Doctor was summoned before the Time Lord Council. To his and Barusa's surprise, the Master acknowledged the Doctor as his brother and embraced him, offering him a full pardon in the eyes of Gallifreyan law in exchange for going on a few missions on the Time Lords' behalf. The first concerned a species of warmongering cyborg killers who the Master had learned were threatening the outer edges of Gallifrey's galaxy: the Dalek. He sent the Doctor and Barusa back to their home planet Skaro in an earlier time, letting them believe he was tasking them with erasing the Daleks from existence. However, the Doctor actually played an unwitting part in the historically-recorded version of the Daleks' origins. When Davros and his Daleks were about to destroy the Doctor, the Masterinstead swooped in and revealed to the Daleks how Davros had betrayed their ancestors the Kaled. The Daleks destroyed their creator and pledged allegiance to the Master, who would go on to have them chase the Doctor through time. The Doctor finally detonated the incubator room, though he could not destroy the Master and the already-living Daleks, who continued to pursue them through time.
Eventually, the Doctor and Ulysses] were reunited at last, "with great joy". They returned to Gallifrey, bringing with them "all the strength and curiosity that had been lost… (…) passion and, even more importantly, compassion". With Ulysses to prove his lineage, the Doctor was allowed to replace the disgraced Master as President. (PROSE: The Chronicles of Doctor Who?)
Behind the scenes
The version of The Chronicles of Doctor Who? included in the original Leekley Bible presented an illustration of the rebooted Master. Curiously, he was depicted with the likeness and outfit of the Valeyard. The version of the story which eventually obtained an official release in Doctor Who: Regeneration did not include this illustration.
Although the Doctor and the Master being half-brothers may be perceived as one of John Leekley's most radical departures from established Doctor Who continuity, John Nathan-Turner confirmed on the DVD commentary for Planet of Fire that it was his authorial intent at the time, when Anthony Ainley's portrayal was current, that he was secretly the Doctor's brother. As he burns away in this story, the Master pleads with the Doctor to "show mercy to his own…", but does not get to finish the line. The notion would ultimately be derided in The Sound of Drums where Martha Jones asks the Tenth Doctor if the Master was "his secret brother or something" and the Doctor derisively replies "You've been watching too much TV".