Barusa's universe

The Time Lord Cardinal Barusa recorded the travels of his grandson the Doctor across a version of reality (PROSE: The Chronicles of Doctor Who?) which accounts variously indicated was a parallel universe, (COMIC: Fire and Brimstone) a palimpsest universe, (PROSE: The Infinity Doctors) or a coexisting contradictory layer of the "conventional" Eighth Doctor's reality. (PROSE: Unnatural History, The Gallifrey Chronicles)

Origins
By one account, this reality was one of the infinite parallel universes which made up all that was possible, the realm Daleks termed "possible space". (COMIC: Fire and Brimstone) Other accounts would support this, with one suggesting that the Spider Daleks of Barusa's universe were a possibility which Davros of the Doctor's universe considered but did not pursue. (PROSE: Father of the Daleks)

By another account, this reality was not a parallel universe but instead a version of the Doctor's universe created by the ever-shifting nature of history, overwriting previous palimpsest universes. (PROSE: The Infinity Doctors)

During the Last Great Time War, Time Lord attempts to change Dalek history to prevent the creation of the Daleks only resulted in every single created possibility creating new stranger versions of Daleks, including Spider Daleks. (PROSE: Engines of War)

General outline
In this universe, the Time Lord were founded millenia prior to the Doctor's era by Rassilon. Rassilon prophesised the Doctor's life in the Scrolls of Rassilon, which were buried with him in the secret Tomb of Rassilon protected by the Outcasts. Time Lords lived in the Domed City of Gallifrey, whose "resonating crystals" contained dead souls of Time Lords as a form of immortality. Barusa's son, Ulysses, was an explorer who had two sons: the Master and the Doctor. The Master was of fully Time Lord blood, but the Doctor had a human mother Annalise, leading to the Doctor's parentage being hidden.

800 years after the Doctor was born, when he was in his eighth incarnation, the Doctor found the lost Scrolls of Rassilon as Barusa neared death and the Master was poised to rule Gallifrey. The Doctor came to Barusa on his deathbed and Barusa revealed to him the truth of his parents. As President, 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 death, during which his soul left his body and unexpectedly found itself drawn to the Doctor's TARDIS, merging with it and becoming the Doctor's companion in the quest to find Ulysses. (PROSE: The Chronicles of Doctor Who?)

The Daleks of this reality had a spider-like appearance which exposed their mutant form, which was insectoid but also more recognisably humanoid than the Dalek mutants of the Eighth Doctor's universe. (COMIC: Fire and Brimstone) The Doctor and Barusa first encountered the Daleks at their genesis on Skaro, trying to stop Davros from creating them. The Doctor found himself unable to do this, and 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 and Barusa continued looking for Ulysses through time and space in the The Doctor's TARDIS, now pursued by the Daleks. They went on many adventures, including encounters with the pirate Blackbeard in 18th century Spain — who turned out to have been Ulysses in disguise —, the war criminal Magnus Greel in 20th century New York City, the marauding cyborgs know as the Cybs, an alien who has merged with a light-house keeper in 1906, an "evil force" known as the Toymaker, the gunslinger Doc Holliday, a group of Neanderthals in Tibet, and with a colony ship where the whole population of the future Earth is frozen in cryo-stasis, only to be preyed on by parasitic insect creatures.

Eventually, the Doctor and Ulysses were reunited at last. With Ulysses to prove his lineage, the Doctor was allowed to replace the Master as President and wear the Sash of Rassilon. In subsequent years, however, the Doctor still occasionally snuck away from his duties aboard the TARDIS to engage in further adventures, just for the fun of it. (PROSE: The Chronicles of Doctor Who?)

Fate
By some accounts, this reality was overwritten by the shifting of time, becoming a palimpsest universe whose traces contributed to the Doctor's reality being "riddled with paradox and contradiction". (PROSE: The Infinity Doctors)

Relation to other realities
Existing in parallel, this universe intersected with the Eighth Doctor's by chance when a spatial rift in the Magellan Cluster allowed a Dalek ship from this universe to enter the Eighth Doctor's. There, the alternative Daleks came into conflict with the Dalek Hive. The Hive Daleks were terrified by the potential of their parallel counterparts, who took months to subdue even with all of the Dalek Hive's resources. This led the Supreme Dalek to mastermind a preemptive strike on the alternate universe, taking control of the engineered sun known as Crivello's Cauldron in order to turn it into a wormhole that would allow the Daleks to conquer the rest of the Multiverse. However, in the few seconds after the portal opened but before the Dalek Hive could cross it, more Spider Daleks came through on the attack (with a group managing to destroy the Supreme Dalek himself), alongside a swarm of Great Vampires from another universe. (COMIC: Fire and Brimstone)

The Infinity Doctor's reality was subsequent to this reality's palimpsest existence. The Infinity Doctor, in realizing the shifting nature of history, simultaneously remembered multiple versions of his past, including one where his mother was Annalisse. Additionally, one of the Doctor's core memories was of finding something important in a secret mountainous cave. (PROSE: The Infinity Doctors)

Another perspective showed that this reality existed as one of many loose strands in the Eighth Doctor's biodata, being one of many overlapping pasts and futures constantly shifting around the Doctor's present during his travels with Sam and Fitz. Griffin the Unnaturalist observed this strand and described it as one where the Doctor was "a hero with wild ideas about a quest," offering it as one of several he could isolate into being the only reality so that he could to simplify the ambiguity and complexity of the Doctor's life. Following this, Sam Jones distracted Griffin by making up a prophecy that the Doctor was a half-human who would save the universe from a Time of Darkness with the help of a "wise old spirit who guides him"; the Doctor would later act as if this was genuine secret knowledge Sam shouldn't have known, and was glad that she made it up. (PROSE: Unnatural History)

Marnal once observed the Eighth Doctor to have a chaotic non-linear timestream defined by “temporal orbits, retcons, paradoxes, parallel time lines, reiterations, and divergences.” (PROSE: The Gallifrey Chronicles) Barusa travelled with his reality’s Eighth Doctor and almost all of their adventures were reiterations of events from the First to Seventh Doctors' lives. (PROSE: The Chronicles of Doctor Who?) The source involving Marnal also depicted the Doctor's father as being named "Ulysses", and showed that at the time of the Doctor's birth there was a prophecy that a Time Lord would "find the lost scrolls of Rassilon and lead Gallifrey from darkness." (PROSE: The Gallifrey Chronicles)