What is the scar on Joaquin Phoenix's lip?

If you mean the scar on his lip, it is due to a cleft pallet

More info. Some relevant medical specialists believe its as result of of unilateral microform cleft.

Here is the correct answer as given on Spike TV:

"The scar between Joaquin Phoenix's lip and nose is obvious. It practically had second billing in Gladiator. It has long been thought that Joaquin was born with a cleft lip and the scar is the result of corrective surgery. This is not so. Rather, Joaquin was born with the scar. The scar developed while Joaquin was in his mother's stomach. It is known as a microform cleft, a mild form of a cleft lip. A "microform cleft can appear as small as a little dent in the red part of the lip or look like a scar from the lip up to the nostril," as in Joaquin's case."

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