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We perform a time-dependent amplitude analysis of $B^0 \to K^0_S\pi^+\pi^-$decays to extract the CP violation parameters of $f_0(980) K^0_S$ and$\rho^0(770) K^0_S$ and the direct CP asymmetry of $K^{*+}(892) \pi^-$. Theresults are obtained from a data sample of $(383 \pm 3) \times 10^6$ $B\bar{B}$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 combinedconfidence interval for values of the CP parameter $\beta_{eff}$ in $B^0$decays to $f_0(980) K^0_S$ is $18^o < \beta_{eff} < 76^o$ at 95% confidencelevel (C.L). CP conservation in $B^0$ decays to $f_0(980) K^0_S$ is excluded at$3.5\sigma$ including systematic uncertainties. For $B^0$ decays to$\rho^0(770) K^0_S$, the combined confidence interval is $-9^o < \beta_{eff} <57^o$ at 95% C.L. In decays to $K^{*+}(892) \pi^-$ we measure the direct CPasymmetry to be $A_{CP}=-0.20 \pm 0.10 \pm 0.01 \pm 0.02$. The measured phasedifference (including $B^0\bar{B}^0$ mixing) between decay amplitudes of $B^0\to K^{*+}(892) \pi^-$ and $\bar{B}^0 \to K^{*-}(892) \pi^+$, excludes theinterval $-137^o < \Delta\Phi(K^{*+}(892) \pi^-) < -5^o$ at 95% C.L.

Time-dependent amplitude analysis of B0 --> K0S pi+ pi-