Time-dependent amplitude analysis of B(0)-> K(S)(0)pi(+)pi(-)

We perform a time-dependent amplitude analysis of B(0)-> K(S)(0)pi(+)pi(-) decays to extract the CP violation parameters of f(0)(980)K(S)(0) and rho(0)(770)K(S)(0) and the direct CP asymmetry of K(*+)(892)pi(-). The results are obtained from a data sample of (383 +/- 3)x10(6) BB decays, collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. We find two solutions, with an equivalent goodness-of-fit. Including systematic and Dalitz plot model uncertainties, the combined confidence interval for values of the CP parameter beta(eff) in B(0) decays to f(0)(980)K(S)(0) is 18 degrees <beta(eff)< 76 degrees at 95% confidence level (C.L). CP conservation in B(0) decays to f(0)(980)K(S)(0) is excluded at 3.5 standard deviations including systematic uncertainties. For B(0) decays to rho(0)(770)K(S)(0), the combined confidence interval is -9 degrees <beta(eff)< 57 degrees at 95% C.L. In decays to K(*+)(892)pi(-) we measure the direct CP asymmetry to be A(CP)=-0.20 +/- 0.10 +/- 0.01 +/- 0.02. The measured phase difference (including B(0)B(0) mixing) between decay amplitudes of B(0)-> K(*+)(892)pi(-) and B(0)-> K(*-)(892)pi(+), excludes the interval -137 degrees <Delta Phi(K(*+)(892)pi(-))<-5 degrees at 95% C.L.