With a sample of about 227x10(6) BB pairs recorded with the BABAR detector we perform a full angular analysis of the decay B0-->phiK(*0)(892). We make novel measurements of five parameters sensitive to CP violation. We also measure the branching fraction to be (9.2+/-0.9+/-0.5)x10(-6) and determine the fractions of longitudinal and parity-odd transverse contributions as f(L)=0.52+/-0.05+/-0.02 and f( perpendicular)=0.22+/-0.05+/-0.02. The phases of the parity-even and parity-odd transverse amplitudes relative to the longitudinal amplitude are found to be phi( parallel)=2.34(+0.23)(-0.20)+/-0.05 rad and phi( perpendicular)=2.47+/-0.25+/-0.05 rad. We also observe the decay B0-->phiK(*0)(1430).