The DoctorDonna

The DoctorDonna was a composite being created when Donna Noble touched the Tenth Doctor's regeneration energy affected severed hand and sparked a "two-way biological meta-crisis". She retained Donna Noble's personality and physical appearance, but also had all of the Doctor's memories and intelligence. After the Doctor locked her away inside Donna's subconscious because Donna's human brain could not bear the strain of the Time Lord cognition, she continued to "fight for [them]", sending Donna's conscious minds hints which helped the Doctor and Wilfred Mott foil Joshua Naismith and 's plans.

A day to come
When Donna and the Doctor travelled to the Ood Sphere in 4126 and discovered the Ood's servitude was caused by the removal of the Ood's forebrain and the "third element", the controlling Ood Brain, being blocked. They together unblocked the Ood Brain, ending the chaos between the Ood and humans running the Sphere. The suffering that the Ood went through combined with witnessing Klineman Halpen get turned into an Ood was too much for Donna, who said she wanted to go home; she later calmed down and took this statement back, however. When they parted, Ood Sigma referred to Donna as "DoctorDonna". Neither the Doctor nor Noble realised the significance of the statement at the time, (TV: Planet of the Ood) but after the meta-crisis occurred, the Tenth Doctor realised that the Ood had "seen [the meta-crisis] coming" due to the timelines converging on the products of the meta-crisis, the DoctorDonna and the meta-crisis Doctor, leading to premonitions of their coming rippling backwards in time. (TV: Journey's End)

The meta-crisis
Much later, Noble and the Tenth Doctor rushed to Earth in 2009, only to find it taken from underneath them. They then went to the Shadow Proclamation for help. They traced the Earth, along with twenty-six other missing planets, to the Medusa Cascade, where the planets had been hidden by being placed one second out of sync with the rest of the universe. As the Doctor reunited with Rose Tyler, his former companion, he was shot by a Dalek and rushed into the TARDIS with Rose, Jack Harkness, another companion, and Donna. As a result, the Doctor began regenerating but was able to use some of the regeneration energy to heal himself before funnelling the remaining energy into a matching bio-receptacle — his spare hand — and stop the regeneration. (TV: The Stolen Earth)

The TARDIS was taken on board the Crucible and its defences were taken down. Donna was separated from the Doctor when the TARDIS refused to let her leave when the others surrendered to the Daleks. Donna reached out toward the Doctor's hand when the TARDIS was being sent to the core of the Crucible to be destroyed. The regeneration energy stored in the Doctor's hand interacted with Donna and created a being who looked like the Doctor but was half human and had aspects of Noble's personality. Some of the Doctor's biodata, in the form of a copy of his mind (including his memories and his Time Lord intellect) was transferred into Donna at the same time, as the meta-crisis was "two-way", but at first it "laid dormant" inside the still-human Donna. (TV: Journey's End)

The DoctorDonna comes to life
When Donna tried to use the Meta-Crisis Tenth Doctor's Z-Neutrino Biological Inversion Catalyser on the Daleks, Davros electrocuted her. The electrical shock on Donna gave her synapses a "little extra spark", "kicking [the DoctorDonna] into life". Jubilant at the abilities at her disposal, the DoctorDonna quickly used her new-found intellect to deactivate the reality bomb and disable the circuitry on the Daleks' controls and helped use the magnetron to bring twenty-six of the planets back to their rightful places in the universe. The Meta-Crisis Doctor, fulfilling one of Dalek Caan's prophecies, destroyed the Daleks. When the Supreme Dalek wrecked the magnetron, Earth was the last planet still in the Cascade. The DoctorDonna helped the Doctor and his companions to "tow" the Earth to its proper place in the galaxy with the TARDIS.

After assisting the Doctor in exiling the Meta-Crisis Doctor to Pete's World and saying farewell to Rose, the DoctorDonna's brain overloaded, with her and the Doctor both recognising that the reason no human-Time Lord meta-crisis had been recorded before was that they were not viable, and the DoctorDonna's overload of cognition was slowly killing Donna's human body. The DoctorDonna begged the Doctor to let her die as she was, but the Doctor chose instead to lock away all the information relating to himself in Donna's brain — restoring Donna's original human mind and allowing her to survive, but also wiping away her memories of her pre-meta-crisis travels with the Doctor, and meaning that their travels together had to come to an abrupt end lest the extraordinary things she saw, and the sight of the Doctor himself, reawaken Donna's locked memories and, with them, the DoctorDonna and the death sentence threat she represented. (TV: Journey's End) The Doctor also implanted a "defence mechanism" inside Donna's mind in the form of a shockwave of regeneration energy that would put her and everyone in her vicinity to sleep if she started to remember, before the DoctorDonna could fully awaken and kill her. (TV: The End of Time)

Inside Donna's subconscious
On Christmas Day, turned every human into versions of himself. Noble's half-Time Lord mind caused her not to transform. The shock of seeing her mother and Shaun Temple transformed into duplicates of the Master reawakened some of the memories of her travels with the Doctor. Visions of aliens she had met appeared in her mind. She called her grandfather Mott and was told to run for her life. She ran, but was cornered by Master duplicates in an alley, and was beginning to break down over the rush of recovered memories. However, the Doctor had also implanted a form of mental self-defence in her mind that released a blast of energy, putting Noble to sleep and knocking the Master facsimiles unconscious. (TV: The End of Time)

Legacy
A Time Lord author learnt of the DoctorDonna while doing research for his book and briefly considered that she might have been the Hybrid of Gallifreyan legend but ultimately dismissed the idea as her story didn't fit the prophecy. (PROSE: A Brief History of Time Lords)