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In The Christmas Invasion, The Doctor was within 15 hours of his regeneration cycle, so he was able to regrow his hand after the Sycorax cut it off. If he was decapitated within that period of time, would he regrow a new head, body, or would two new Timelords come about?

If possible canon answers, please.

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The Time Lord Would Die

Brain death is one of the few things called out specifically to cause a regeneration to "fail". From the wikia:

The Fifth Doctor once noted that the important thing in regeneration was that the brain remain intact, with an early Gallifreyan being killed for good when she was shot in the brain to prevent regeneration.

The instance occurs during the novel Cold Fusion.

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A Timelord can regenerate their head after being decapitated.

In the canon prose story "Shadows of Avalon", the Galifreyan secret agent Cavisadoratrelundar is in the process of regenerating a new head (from the neck upwards) after being decapitated. The process only stops after both her hearts are pierced.

The blow connected. Cavis’s head broke from her body. It flew over the battlements. Mab completed the sweep of her sword. Cavis’ body fell to its knees. Then collapsed on to its front. Some sort of energy was streaming from the corpse’s head, swirling about something that was quickly developing there, as if a new head was swiftly being formed where the old one had been. Mab stepped forward and stabbed her sword down twice. Once for where there was a heart, and once for where one was about to be. The outrush of energy ceased. Cavis lay still.

It should be noted though, that this was a fresh regeneration whereas in the "Christmas Invasion" episode the Doctor only has enough energy to regrow his hand. There's no in-universe explanation of whether regrowing a head requires more energy than a hand but I think we can reasonably assume that it does;

DOCTOR: And now I know what sort of man I am. I'm lucky. Because quite by chance I'm still within the first fifteen hours of my regeneration cycle, which means I've got just enough residual cellular energy to do this. (He grows a new hand.)

In short, my guess is no. He would (probably) have had insufficient energy left 15 hours after regenerating.

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