Auld Mortality's universe

In a parallel universe, the Doctor pursued a career as an author before leaving Gallifrey with an alternate version of his granddaughter Susan. During this time, the Time Lords had become increasingly corrupt as the centuries passed, and their Lord Presidents began dying during their terms. This universe's version of Quences brainwashed the Doctor into becoming the next Lord President, but the Doctor was not interested. (AUDIO: Auld Mortality)

After leaving Gallifrey, the Doctor was pursued by the Time Lords, like Agent Zeuro, because of his meddling in history. He saved the princes from the tower, took Leonardo da Vinci with him on his travels, and he gave Beethoven a hearing aid among other cases. (AUDIO: A Storm of Angels)

Relation to other realities
Using the Possibility Generator, the Doctor was able to view other possible realities. In his rose garden, he kept a Possibility Tree representing the infinite tangled possibilities birthed all from the Aurora Temporalis, sometimes glimpsing another version of himself travelling in an old TARDIS.

The Tree also showed other versions of Gallifrey, including some where the Time Lords were "as steeped in blood as we are steeped in dust" or were ruled by sorcery instead of science, as well as one where the world was cursed and all the children died. (AUDIO: Auld Mortality) This third reality involved a similar yet parallel version of the Doctor and Susan's escape from Gallifrey. (PROSE: Lungbarrow)

Continuity with the Doctor's broader reality
At the end of this version of the Doctor's escape from Gallifrey, he asked Susan to come with him. The Possibility Generator detected several branching timelines in which she agreed, including one where the Doctor and Susan came to live in Totter's Lane and one where the Doctor and Susan came to live in Barnes Common. However, other parallel possibilities involved Susan saying no, (AUDIO: Auld Mortality) and further accounts showed this Doctor living a parallel version of the First Doctor's life in which Susan declined and the Doctor subsequently never met Ian Chesterton and Barbara Wright. (AUDIO: A Storm of Angels, PROSE: The Innocents)

An individual resembling the First Doctor, existing in the universe where Doctor Who never took off, once mused that he'd once either been a writer or dreamed of being a writer. (PROSE: All Our Christmases)