Searches for lepton-flavor-violating decays of a tau lepton to a lighter mass lepton and a photon have been performed with the entire data set of (963+/-7)x10{6} tau decays collected by the BABAR detector near the Upsilon(4S), Upsilon(3S) and Upsilon(2S) resonances. The searches yield no evidence of signals and we set upper limits on the branching fractions of B(tau{+/-}-->e{+/-}gamma)<3.3x10{-8} and B(tau{+/-}-->mu{+/-}gamma)<4.4x10{-8} at 90% confidence level.
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