The Dalek that emerges from the Squire is still the Squire. It's not a separate being.
Shada's computer system claimed that the Squire was a time anomaly, and had no history. (COMIC: The One) The Squire was in fact a member of the Volatix Cabal, but was unaware of her true nature. (COMIC: Fast Asleep)
The Time War Edit
During the Last Great Time War, the Squire was planted by the Volatix Cabal with the War Doctor, serving as his companion. (COMIC: Gently Pulls the Strings) The Doctor introduced her to the prose of Marcel Proust. (COMIC: The Then and the Now) The Squire was with the Doctor when he led a Shrikefleet against a Plasma-Wheel armada on Vexa; held the line against six Barrage-Leks and routed the exotic plunder at the chronofracture on Borun, and threw down the Heisenberg mutations on Kether Prime. (COMIC: Pull to Open)
The Doctor sent the Squire to save Alice Obiefune, who had been captured by the Volatix Cabal. She burst her way into their stronghold and killed all of its inhabitants. The Squire then accompanied the War Doctor and his associates to Golgauth, where they were attacked by a Cyclor. (COMIC: The Organ Grinder) Whilst escaping from the Cyclors, Alice stole the Psilent songbox from the Doctor. The Squire and the Doctor set off in chase. The Squire caught up to Alice and saved her from one of the Volatix by slicing it in half with her sword. Alice then activated the Songbox, which reacted with a paradox created by the Master and caused a chronal meltdown. (COMIC: Kill God) A member of the Volatix Cabal merged itself with the ensuing paradox, creating the Malignant. (COMIC: Fast Asleep) The wave of the paradox swept the Squire to places unknown, where she forgot who and what she was. (COMIC: Gently Pulls the Strings)
Travelling with the Eleventh Doctor Edit
The Squire wandered the universe, lost for a thousand years, until she located the Doctor again. (COMIC: Gently Pulls the Strings) She met the Eleventh Doctor, vowing to protect him once more. She saved him and Alice Obiefune from a group of beings who put him on trial for his actions during the Time War. The trio escaped into the TARDIS, where they were confronted by Abslom Daak. (COMIC: The Then and the Now)
The Squire accompanied the Doctor to Veestrax, where they were attacked by robotic spiders. The Squire and Daak destroyed the spiders. (COMIC: Outrun) She later helped the Doctor to subdue the soldiers guarding River Song's prison cell. (COMIC: The Judas Goatee) River helped the group gain access to Shada, where the Doctor sought the Master's TARDIS. The Squire was the only one able to free the Doctor and his companions from imprisonment on Shada, as the prison's AI believed that she did not exist. (COMIC: The One)
After leaving Shada, the Squire questioned the Doctor on why he was in the company of so many companions. The Squire disliked the Doctor's answer, believing herself to be worthless to him. (COMIC: Downtime) She decided not to leave the Doctor forever, however, and decided to hunt The Then and the Now through time, following it to Lujhimene where she encountered the Doctor again. The Squire was wounded while fighting the Then and the Now. The Doctor took her to the TARDIS and hooked her up to a medical machine to heal her. (COMIC: Running to Stay Still) Despite the machine being capable of healing her injuries, the Squire began to flatline, and the Doctor was unable to get her heart working again. (COMIC: First Rule)
The Squire soon awoke, remembering her Dalek origins, and shot Abslom Daak, nearly killing him. She then directed her weapon at the Doctor as the Volatix Cabal Dalek within her emerged from her flesh and spoke through her lips in its own voice. (COMIC: Fast Asleep)
The Eleventh Doctor tried to appeal to the Dalek Squire, who mournfully confessed that it had not merely deceived the Doctor, but tried its hardest to try to be the Squire and renounce its nature; however, it reflected that "destiny" would not have allowed it. The Dalek-awakened Squire then took the Doctor back to the Overcaste who intended to try and execute him for ending their gods, demanding to collect the "nice big bounty" on his head and ignoring their questions about "her" changed appearance. The Squire's true purpose, however, was to summon the the Malignant in a swarm, something the Dalek Squire saw as another manifestation of "destiny". The Squire grew more and more Dalek-like in appearance over the course of the ensuing confrontation, during which it explained the ultimate fate of the Volatix Cabal and the Cyclors (who had fused into the Malignant).
On this information, the Squire set out to exterminate the Overcaste; this would sever the psychic link tying the Cyclors to the universe, therefore leaving only the Dalek side of the Malignant wielding the Malignant's powers — beginning the "Age of the Dalek Gods". The Squire briefly succeeded in bringing the Dalek Gods into existence, but as it gloated, Abslom Daak (healed by the TARDIS) burst out the TARDIS door and crushed the Squire against the ground with his vehicle. As the Squire lay dying, sputtering the Volatix mantra "Exterminhate" with more confusion than anger, the Eleventh Doctor tried to give his former companion a last chance, arguing that it was his firm belief that anyone "could be more than their programming". After a moment's silence, the Squire reacted by trying to blast the Doctor with its laser gun, shouting "EXTERMINH-", an action it never finished as River Song disintegrated what was left of it with her own weapon. (COMIC: Gently Pulls the Strings)
The Squire wore combat armour, including Quantum gauntlets made of Gallifreyan steel. (COMIC: The Then and the Now) When she was young, she had blond hair. (COMIC: The Organ Grinder) When she was exposed as a Volatix agent, the Squire grew a Dalek eyestalk in her mouth and a light indicator in her right eye. (COMIC: Gently Pulls the Strings)