House of Rassilon

Rassilon was a member of an ancient Family (PROSE: Gallifrey - Notes on the Planet's Background) which continued into the modern as the House of Rassilon after it became a Great House. (AUDIO: Desperate Measures)

Some accounts indicated this bloodline was connected to the Doctor's family directly (PROSE: The Chronicles of Doctor Who?) or via adoption, (PROSE: Birth of a Renegade) although others indicated the Doctor's family was firmly separate (PROSE: Gallifrey - Notes on the Planet's Background) and instead had a connection to the Founders of Gallifrey via the Other. (PROSE: Lungbarrow)

Early history
Rassilon's father had been a suet shredder. It was Rassilon who brought success to his bloodline when he became a Gallifreyan Hero. (PROSE: Cat's Cradle: Time's Crucible)

By some accounts, Omega was Rassilon's cousin. (PROSE: Remembrance of the Daleks, Gallifrey - Notes on the Planet's Background) The two of them collaborated in ensuring the bloodline's survival following Pythia's curse, changing the Rassilon Family into a Great House. From this point forwards, like all other Houses, the House of Rassilon would use its loom to have a set number of cousins with recycling traits. (PROSE: Gallifrey - Notes on the Planet's Background)

Modern era
By one account, Susan Foreman was a descendant of Rassilon. (PROSE: Birth of a Renegade)

In Barusa's universe, Barusa, Ulysses, the Doctor, and the Master were all direct descendants of Rassilon. (PROSE: The Chronicles of Doctor Who?)

During the Last Great Time War, Valerian belonged to the House of Rassilon. Valerian could trace his lineage back to Rassilon himself. (AUDIO: Desperate Measures)

Behind the scenes

 * Similar to claims of Rassilon descendance, the choose-your-own-adventure-style novel Search for the Doctor has the Doctor discover he is a direct descendant of Omega. Given Ben Aaronovitch's perspective that Omega was a member of Rassilon's family, one could also connect this to the House of Rassilon.