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Unlike his immediate predecessor, who was plagued by melancholy due to his actions during the Last Great Time War, the Tenth Doctor possessed an outgoing, lively and genial demeanour that hid his "survivor's guilt". For most of his incarnation, he was able to successfully project a convivial and even frivolous front. However, when he had to engage in conflict, the Tenth Doctor's energies would shift toward heroism to reveal a fiercely protective man who resolutely guarded what he held dear, and who could be viciously unforgiving to the forces that dared menace them.
Intentionally or not, this incarnation showed a definite ability to flirt successfully with humans, such as Madame de Pompadour and his eventual wife Elizabeth I. His personal magnetism was so pronounced that some women, like Clare Pope and Christina de Souza, proactively came on to him. Jack Harkness readily admitted his attraction as well.
Late in his life — and especially when he was travelling without companions — the weight of being the last Time Lord became much more pronounced. If prodded too much, he would erupt in an almost righteous sense of fury. Indeed, as compared to the Eleventh Doctor, the Tenth Doctor was described by the Moment as "the man who regrets". The fact that he was instantly able to recall the number of Gallifreyan children that he believed an earlier life had killed during the war indicated just how keenly he actually felt those horrendous memories.
He travelled mainly with three companions: Rose Tyler, Martha Jones and Donna Noble. Each relationship was shaped, to one degree or another, by romance. He seemed to genuinely love Rose as the person who helped heal some of the scars of the Time War; he was completely oblivious to Martha's obvious affections toward him, and he insisted upon a platonic relationship with Donna. After he was compelled to wipe Donna's memory completely, he entered a period in which he shunned long-term companions altogether — making an exception only for Majenta Pryce, who essentially forced her way into the TARDIS.
He met his end after he absorbed a huge quantity of nuclear radiation whilst saving the life of Donna Noble's grandfather, Wilfred Mott. The foreknowledge of his own demise and his strong attachment to the memories and romance he had that were special to this version of himself made it a particularly difficult task for the Doctor to let go of this incarnation.
Biography from the TARDIS Data Core article, licensed under CC-BY-SA
Rose Tyler, Mickey Smith, Donna Noble, Martha Jones, Captain Jack Harkness, Astrid, Sarah Jane Smith, Jackson Lake, Rosita Farisi, Lady Christina de Souza, Adelaide Brooke, Wilfred Mott
Notes for The Doctor