The Dominie

The Professor, also known as the Dominie, (PROSE: The Choice) was an individual who travelled in space and time with Ace in the Cosmos. Despite his human appearance, he claimed that his biology wasn't human and that he was centuries old. (PROSE: Republica) His timeline and the universe around him were constantly being rewritten, something he was generally aware of. (PROSE: Republica, The Choice)

Origins
The Dominie described himself as a fourth-dimensional being. Because of this, he remembered several different pasts and futures, as well as multiple alternative presents, including ones where he travelled with "archaeologists and androids". (PROSE: The Choice)

Travels with the Mistress
In some past life which may not have corresponded exactly to his specific timeline, the Dominie remembered knowing a version of the Mistress, whom he greatly admired. He kept a picture of her in a silver locket. (PROSE: The Choice)

Indeed, at some point before her adventures in Ecto-Space, the Mistress remembered travelling with a man whom she trusted absolutely. She would later state that "I was ready to give up my life for him. I thought it would last forever. That we would go on forever, as we were". Her travels with him and K9 apparently involved a lot of "recky". (AUDIO: The Choice) On one occasion, the Mistress and her "mentor" took a holiday in 19th century Imperial Russia where they learned ballet dancing from Charles Didelot and thwarted the plans of warmongering interdimensional beings known as the Iele. (PROSE: The Choice)

The Mistress eventually left her mentor; unable to return to her original home due to the way her travels with him had changed her, she felt she had no choice but to move on to Ecto-Space in the company of a K9 unit. While delirious due to a fever, she seemingly repeated words from their separation: "But that's just it. Time to choose. I have to be my own--". (AUDIO: The Choice) These words echoed those of the Time Lady Romana when she split up with the Fourth Doctor and moved to E-Space with K9 Mark II: "But it is, isn't it? A moment to choose. I've got to be my own Romana". (TV: Warriors' Gate)

According to B.E.S., the legends about the Mistress mentioned that she oncde had "a mentor of sorts" who showed her "the wonders of her old universe" until "one day, she decided to go at it alone", protecting Ecto-Space "ever since". (AUDIO: B.E.S. Begins)

Travels with Alice
In his version of reality, the Dominie, travelled with a woman called Alice, (PROSE: The Choice) who usually went by the name of Ace, in the Cosmos. At this point, he usually went by "the Professor". The Professor and Ace once visited 1990s England only to discover that history had been dramatically altered by an escaped Ithacan criminal known as LeCompte. Convincing Oliver Cromwell to appoint John Lambert as his successor instead of Richard Cromwell, LeCompte had allowed Cromwell's Protectorate to survive for centuries, meaning that this late-20th-century England remained a totalitarian republic ruled by a Lord Protector. The Professor and Ace further discovered the truth about LeCompte's origins, and that he was actually trying to steer Earth's technological development so that he could direct its military forces back at his homeworld in revenge for his exile. However, realising that (unbeknownst to LeCompte) the wormhole back to LeCompte's homeworld was also a time rift, the Professor tricked him into his own doom by allowing him to fire the war rocket Behemoth through the wormhole, laying waste to the past version of Ithaca, killing LeCompte's past self, and consequently cancelling out his alterations to the timeline. Ace was horrified at the Professor destroying this version of history, aberrant as it was.

Some time later, the Professor and Ace visited a temple built on a "weak point in the linear universe", whose clerics were instantly aware that many timelines overlapped over Ace. She was given a glimpse of her and the Professor's adventures bringing down the Protectorate, and was disturbed to realise that she did not remember anything about the event. When she rejoined the Professor, he confessed that he didn't remember either, and moreover, had not been aware that his history had been rewritten, even though he usually did. Ace asked if a mysterious "him" they'd defeated in the past "after all this timeline rubbish" was to blame, while the Professor was more evasive, stating that there were others who could "meddle with things". They had a heart-to-heart about the moral weight of people from aberrant timelines, with the Professor reaffirming that "everyone mattered" even if they were native to unstable timelines. (PROSE: Republica)

On Jokastarna
Travelling alone under the name of "the Dominie", he made his way to Ecto-Space. He discovered the horrors that had taken place on Jokastarna under Emperor Lukor's regime, and which had been exposed by his old associate the Mistress. He was unable to alter history to prevent the genocide of the caveys, but decided to help steer the destiny of the post-Lukor, parliamentary Jokastarna. He knew that a lecture by a surviving cavey, Tris'Tean, given at the University of Arintanqex would be decisive in Ecto-Space's other residents condemning Lukor's old regime once and for all. He knew that a surviving Lukor loyalist, Duke Erukin, would attempt to assassinate Tris'Tean at the lecture. After dealing with other Lukor loyalists a week after the lecture, he went back in time to before the lecture and met with Tris'Tean, warning him about the assassination attempt and telling him how to avert it. (PROSE: The Choice)

Physical appearance
The Dominie appeared as "a little man in a dark, buttoned-up yellow coat, wearing a matching tartan scarf". (PROSE: The Choice) During his travels with Ace in an alternative England, he wore a "slouchy brown coat" but also had the tartan scarf. He had grey eyes, (PROSE: Republica) and brown hair streaked with gray. (PROSE: The Choice)

Behind the scenes
The Professor was one of the two titular protagonists of The Time Travellers, one of the two subseries of BBV Productions' Audio Adventures in Time & Space. Portrayed by Sylvester McCoy, he was strongly implied to be the Seventh Doctor. Various people involved, including McCoy, felt they were too blatant a copy of Doctor Who and the BBC would send a legal warning over it. The second series of audios would rename him the Dominie, a suggestion by McCoy himself (Scottish for "teacher or master", according to Nigel Fairs). (REF: Downtime – The Lost Years of Doctor Who)

The 2021 novelisation of Republica (the first Time Travellers story) tied itself to the licensed DWU via the licensed usage of Doctor X. It notably presented an alternative possibility for the Professor's identity instead of the BBC Doctor: near the end of the novelisation, the Professor says they need to get "back to the Cosmos", the spacecraft of Doctor Omega. However, the implication is that the framing story seen in the Prologue and Epilogue features versions of Ace and the Professor from another version of their timeline, with the window where they were "the Professor" and "Alice" travelling in the "Cosmos" being the result of alterations to time by an unknown party. More specifically, it could be interpreted as taking place in the timeframe of the Virgin New Adventures, at some point after No Future, with the "real" Seventh Doctor and Ace: when she learns that she and the Professor had to deal with a rewritten version of Earth that ultimately had to be destroyed to restore the normal course of history, Ace thought that they'd already dealt with an unspecified "him" after "all this timeline rubbish", and the Doctor's reply states that there are others who "meddler". This appears to refer to their encounter with the Meddling Monk and the Silurian Earth incident.

"That's the trouble with being a fourth-dimensional being, too many universes and timelines to keep track of. One minute I’m traveling with archaeologists and androids, the next I’m traveling with a woman called Alice."

- Epilogue to The Choice

2022's novelisation of The Choice added an epilogue featuring "the Dominie". There, he casually mentioned that as a fourth-dimensional being, he was aware of multiple overlapping versions of his life, which came with different names. He contrasts the version of himself who travels with "a woman called Alice" (the "BBV Ace") with the version who travels with "archaeologists and androids", alluding to the Seventh Doctor's Virgin New Adventures companion Bernice Summerfield and his Death Comes to Time companion Antimony. He also mentioned knowing a version of the Mistress in the past (the Mistress being an analogue to the TV Doctor's Romana II in much the same way the Dominie is an analogue of the Seventh Doctor).