Perpetual regeneration

Perpetual regeneration, also called perpetual bodily regeneration, was a form of regeneration unconstrained by the limits of the regeneration cycle, by some accounts a desirable form of "True Immortality" (TV: The Five Doctors, PROSE: The Five Doctors) and by others a hellish constant mutation. (TV: Mawdryn Undead)

History
According to the Black Scrolls of Rassilon, perpetual regeneration was a modified form of the basic regeneration virus created by Thremix to improve on the virus' many faults. Rassilon's first incarnation immediately murdered Thremix so that only he could have the immortality of never running out of regenerations. Following Rassilon's imprisonment in the Dark Tower, Rassilon continued to live immortally in his tomb. (PROSE: The Scrolls of Rassilon) Other accounts suggested regeneration was initially developed without a regeneration cap and it was restricted artificially, (TV: The Timeless Children) or else that the limit was natural and affected Rassilon in his original lifetime, hence him developing the Matrix to extend his conscious existence in another way. (PROSE: The Legacy of Gallifrey)

Mawdryn and his followers were cursed with perpetual regeneration from their use of a metamorphic symbiosis regenerator. (TV: Mawdryn Undead)

Borusa initiated a Game of Rassilon to find Rassilon's secret of perpetual regeneration. Rassilon gave this immortality to Borusa, transforming him into a living statue. (TV: The Five Doctors)

Handrel attempted to combine Gallifreyan and Vampire DNA to create perpetual regeneration. (PROSE: The Time Lord's Story)

After the Eleventh Doctor was granted what he identified as "a whole new regeneration cycle" by the Time Lords, (TV: The Time of the Doctor) the Twelfth Doctor admitted that he was "not entirely sure" that he would not "keep on regenerating for ever". (TV: Kill the Moon)