Zagreus

 was the name given to an Anti-Time creature that was formed after a mass of anti-time entered the Doctor and became sentient. The name 'Zagreus' was taken from a legend created by the Neverpeople.

History
Legends stated that Rassilon himself destroyed Zagreus when the Yssgaroth came into the Universe in the events around the creation of the Eye of Harmony. It was said by the Neverpeople that when a casket of Anti-Time was detonated at the Capitol, chaos would engulf the Universe and the empire of Zagreus would form. When the Eighth Doctor prevented this event, he absorbed the Anti-Time particles into his own body. He became a dark being and the embodiment of Zagreus. (AUDIO: Neverland)

Life Inhabiting the Doctor
The Doctor's true personality remained intact, though submerged by Zagreus's strength. The TARDIS was fractured into a similar state, torn between its attempt to help the Doctor and its resentment at his willingness to sacrifice it for Charley. While the Doctor tried to regain control of himself, the Zagreus-TARDIS sided with Rassilon to turn the Doctor fully into Zagreus, to serve as Rassilon's assassin in exchange for Rassilon freeing the TARDIS from the Doctor's 'enslavement', the two of them apparently destroying the TARDIS's shell to sufficiently traumatise the Doctor to allow Zagreus to take control. However, the TARDIS' 'good' side retained enough control to generate various holograms based on the Doctor's previous three selves, the holograms helping the Doctor remember who he was.

Despite Rassilon's efforts to reaffirm the Doctor's status as Zagreus, both personalities rebelled against Rassilon's plans, the Doctor refusing to kill while Zagreus refused to be anyone's puppet. With the Zagreus-TARDIS having been destroyed by Charley, Leela and Romana, the Doctor-Zagreus banished Rassilon into the anti-time universe before the good TARDIS was able to provide his companions with a cure to the anti-time energies in the form of pure zero matter, simultaneously restoring the TARDIS's physical form to normal. However, although the zero matter stabilised the Zagreus 'infection' within the Doctor, the Doctor had to remain in the universe of anti-time to prevent the anti-time still within him from destroying the universe. (AUDIO: Zagreus)

Life as Perfection
The anti-time energies were purged from the Doctor by Rassilon when he entered the Divergent Universe. This let Zagreus manifest as an independent spirit. In this form, Zagreus could possess the bodies of the dead, and confronted the Doctor in the body of Perfection, the 'perfect woman' and wife of the most powerful man in the Divergent Universe, Daqar Keep. She tried to trick the Doctor into taking her into the main universe by working with him in the hunt for the Foundary. During this time it enjoyed a flitatious relationship with the Doctor even proposing at one point to repopulate the Divergent universe with their children (as the universe was seemingly facing extinction), her Eve to His Adam. When she used this legend (which only someone from this universe could know) the Doctor saw through her deception but she had already incapacitated Keep and hypnotised Charley by the time he took action. She attempted to escape into this universe in the TARDIS but it was really Keep adopting its form causing her to become trapped in his body for long enough to allow the Doctor and his companions to leave. Now stuck in the Divergent Universe with no hope of escape, Zagreus accepted Keep's proposal that rather than fight they should renew their wedding vows and seize control of their universe. They both stated that it would be very 'diverting'. (AUDIO: The Next Life)

Zagreus Rhyme
Zagreus sits inside your head,

Zagreus lives among the dead,

Zagreus sees you in your bed,

And eats you when you're sleeping.

Zagreus at the end of days,

Zagreus lies all other ways,

Zagreus comes when time's a maze,

And all of history is weeping.

Zagreus taking time apart,

Zagreus fears the hero heart,

Zagreus seeks the final part,

The reward that he is reaping.

Zagreus sings when all is lost,

Zagreus takes all those he's crossed,

Zagreus wins and all is cost,

The hero's hearts he's keeping.

Zagreus seeks the hero's ship,

Zagreus needs the web to rip,

Zagreus sups time at a drip,

And life aside, he's sweeping.

Zagreus waits at the end of the world,

For Zagreus is the end of the world.

His time is the end of time,

And his moment time's undoing.

Alternate lines
During the part three of Zagreus, a couple of alternate/additional lines are recited by the Eighth Doctor and Rassilon:

Zagreus sets the skies ablaze.

The stars his flame a gleaming...

Zagreus is my secret name,

Zagreus is the one to blame,

Zagreus is the Time Lords' shame,

The beast that I've been keeping.

Personality
When the anti-time energies that formed Zagreus left the Doctor they presumably retained their sentience by taking with them the dark aspects of the Doctor's mind that they had helped to create. Despite this, when Zagreus possessed Perfection's corpse it had a very different personality than to when it inhabited the Doctor. In contrast to the ranting and vengeful being it had originally been. In Perfection it was calmer, petulant sometimes and openly flirted with the Doctor; it only showed evidence of what it used to be like when it was imprisoned by Daqar Keep. This suggests that it takes on mannerisms of whatever body it is possessing. (AUDIO: The Next Life)