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http://tardis.wikia.com/wiki/Meta-Crisis_Tenth_Doctor) -All italics are my personal opinion on this-
The Meta-Crisis Tenth Doctor was created as a result of an instantaneous biological Meta Crisis. Regenerative energies present within The Doctor's severed hand combined with the Human DNA of Donna Noble when she touched the hand's casing. Just one of the many reasons to miss Donna Noble. She is the reason I'm here
The force of the reaction shattered the case allowing the energy to regenerate the entire missing body of the Doctor creating a Time Lord/Human hybrid, and keeping Jack from carrying around a hand in a jar a hybrid that possessed one heart; aged as Humans do and with no regenerative ability to avoid death. And thanks so much for bringing that up. Yep, one heart and aging:in fact just the other day I found a gray hair
As a result of growing partially from Donna's DNA the new Doctor inherited parts of Donna's mannerisms Oi! No I didn't!but maintained that he possessed the same memories, thoughts and feelings of the original Doctor up to the point of his aborted regeneration essentially they were the same man with physiological differences. Yes, same everything, almost. I think I'm better looking, personally, but that's just me being vain
However, the original Doctor was quick to point out his new double was born in battle, full of blood, anger and revenge which enabled him to commit genocide against the Daleks; But they had it coming, how could he not see that? They wanted to destroy reality, kill all life, not to mention they are the reason for the death of Gallifrey. I know his bitterness, I have his feelings and yet he wanted to save them. an act the original Doctor greatly condemns after the events of the Last Great Time War. Feeling his new half-Human counterpart was too dangerous to be left to his own devices, the Doctor entrusts him to Rose Tyler taking the two of them back to Bad Wolf Bay in the parallel universe dubbed Pete's World. And while I do appreciate getting to spend all my time with the beautiful Rose Tyler, I am a touch put off about the whole abandonment issue.
The Doctor told Rose that his half-Human self needed her, as he was angry and vengeful like he himself once was when he met Rose as the Ninth Doctor. He told her that she made him better, and now she had to do the same for his other half-Human self. Rose first objected to this at first, insisting that the new Doctor was not really him, despite the Doctor's assurance that they are the same man, NOT the same man and the half-Human Doctor offering to spend the rest of his life with her. Rose then asked both Doctors what the last thing they said to her was when they were originally standing on Bad Wolf Bay. The Doctor was unable to give her a direct answer, only allowing himself to hint: "Does it really need saying?" At this point she turns to the half-Human Doctor and poses the same question, to which he steps forward and whispers the answer his other self could not say in her ear. And I do love her, very much.
Seemingly overcome with the revelation of his answer, Rose grabed the lapels of the half-Human Doctor and pulled him into a passionate kiss, which he reciprocated. And it was a great kiss. In case anyone was wondering The Doctor looked on sadly, yet stoically, for a brief moment before returning with Donna to the TARDIS and leaving the parallel world. As the doors of the TARDIS slam shut, Rose and the half-Human Doctor broke from their kiss. The half-Human Doctor took Rose's hand and watched the TARDIS dematerialize.