Dalitz plot analysis of the decay B-0((B)over-bar(0))-> K-+/-pi(-/+)pi(0)

We report a Dalitz-plot analysis of the charmless hadronic decays of neutral B mesons to K-+/- pi(-/+) pi(0) With a sample of (231.8 +/- 2.6) x 10(6)Y(4S) -> B (B) over bar B decays collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC, we measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for B-0 and (B) over bar (0) decays and determine the corresponding CP-averaged branching fractions and charge asymmetries. The inclusive branching fraction and CP-violating charge asymmetry are measured to be B(B-0 -> K+ pi(-) pi(0)) = (35.7(-1.5)(+2.6) +/- 2.2) x 10(-6) and A(CP) -0.030(-0.051)(+0.045) +/- 0.055 where the first errors are statistical and the second systematic. We observe the decay B-0 -> K*(0)(892)pi(0) with the branching fraction B(B-0 -> K*(0)(892)pi(0)) = (3.6(-0.8)(+0.7) +/- 0.4) x 10(-6) This measurement differs from zero by 5.6 standard deviations (including the systematic uncertainties). The selected sample also contains B-0 -> (D) over bar (0) pi(0) decays where (D) over bar (0) -> K+ pi(-), and we measure B(B-0 -> (D) over bar (0) pi(0)) = (2.93 +/- 0.17 +/- 0.18) x 10(-4).