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We perform an amplitude analysis of the decays B0->phi K^*_2(1430)0,
phi K^*(892)0, and phi(K pi)^0_S-wave with a sample of about 384 million
BBbar pairs recorded with the BABAR detector. The fractions of longitudinal
polarization f_L of the vector-tensor and vector-vector decay modes are
measured to be 0.853 +0.061-0.069 +-0.036 and 0.506 +-0.040 +-0.015,
respectively. Overall, twelve parameters are measured for the vector-vector
decay and seven parameters for the vector-tensor decay, including the branching
fractions and parameters sensitive to CP-violation.