Using a data sample corresponding to an integrated luminosity of 342 fb(-1) collected with the BABAR detector at the SLAC PEP-II electron-positron storage ring operating at a center-of-mass energy near 10.58 GeV, we measure B(tau(-)--> pi(-)pi(-)pi+nu(tau)(ex.K(S0))=(8.83+/-0.01+/-0.13)%, B(tau(-) -->K(-)pi(-)pi+nu tau(ex.K(S0))=(0.273+/-0.002+/-0.009)%, B(tau(-) -->K(-)pi(-)K+nu tau)=(0.1346+/-0.0010+/-0.0036)%, and B(tau(-) -->K(-)K(-)K+nu tau)=(1.58+/-0.13+/-0.12)x10;{-5}, where the uncertainties are statistical and systematic, respectively. These include significant improvements over previous measurements and a first measurement of B(tau(-) -->K(-)K(-)K+nu tau) in which no resonance structure is assumed. We also report a first measurement of B(tau(-) -->var phi(-)nu tau)=(3.42+/-0.55+/-0.25)x10(-5), a new measurement of B(tau(-) -->var phi K(-)nu tau)=(3.39+/-0.20+/-0.28)x10(-5) and a first upper limit on B(tau(-) -->K(-)K(-)K+nu tau(ex.var phi)).