Holo-Doctor

The Holo-Doctor, (PROSE: Infinite Requiem, TV: The Power of the Doctor) also referred to as the holo-me by the Thirteenth Doctor, was an interactive AI hologram  (TV: The Power of the Doctor) that multiple incarnations of the Doctor provided for their companions to consult when they were not available. The hologram could take the form of different Doctors, depending on their emotions and which Doctor the person had known the longest. (PROSE: Infinite Requiem, TV: The Power of the Doctor)

History
The Seventh Doctor once gave Bernice Summerfield a "simple, interactive hologram" of himself that projected from a small pyramid, originally intending to give it to Ace before she left them. Benny considered its realism perfect apart from haziness around the edges, and mentally referred to him as the "holo-Doctor" or "h-Doctor." He wore the Doctor's brown coat, hat, and usual umbrella. (PROSE: Infinite Requiem)

Anticipating that he would be corrupted by the Talent Scout during his takeover of SERVEYOUinc, the Eleventh Doctor provided Alice Obiefune with a hologram of himself in his watch to consult her in a backup plan to regain his senses. It would advise her as she dressed and acted as the Doctor to inspire hope in those being hunted for their creativity in SERVEYOUinc City. (COMIC: The Other Doctor)

The Holo-Doctor was later used by the Thirteenth Doctor to assist her in thwarting the Master's Dalek Plan. The Doctor had planted hologram implants of herself on Yasmin Khan, Tegan Jovanka and Ace, allowing the hologram to appear in close proximity to any one of them. However, as the holograms were affected by their emotional memory, the holograms also took the appearance of the Fugitive Doctor, Fifth Doctor, and Seventh Doctor, respectively.

A hologram of the Fifth Doctor made amends with Tegan Jovanka, reminding her that he never forgot her after they parted company, whilst a hologram of the Seventh Doctor made amends with Ace after their fall out. A hologram of the Fugitive Doctor assisted Yasmin Khan and Inston-Vee Vinder in reversing the Thirteenth Doctor's forced regeneration using the regeneration energy of the CyberMasters, and bore witness to the resulting "forced degeneration" before deactivating. (TV: The Power of the Doctor)

Behind the scenes

 * After some fan confusion, writer Nick Slawicz had to clarify that it was not the Holo-Doctor that appeared in his audio story, The World Tree, but just a live-feed of the Eleventh Doctor that appeared as a hologram.
 * According to the production information text on the Scream of the Shalka DVD, in original drafts of the script, a hologram of the Fifth Doctor was to serve as the TARDIS Defence System; this was changed to the android Master.