Measurements of branching fractions, rate asymmetries, and angular distributions in the rare decays B -> Kl(+)l(-) and B -> K(*)l(+)l(-) RID C-2728-2008 RID C-5223-2009 RID C-5719-2008 RID D-1055-2009 RID A-2675-2009

We present measurements of the flavor-changing neutral current decays B -> K center dot(+)center dot(-) and B -> K-*center dot(+)center dot(-), where center dot(+)center dot(-) is either an e(+)e(-) or mu(+)mu(-) pair. The data sample comprises 229x10(6) Upsilon(4S)-> B (B) over bar decays collected with the BABAR detector at the PEP-II e(+)e(-) storage ring. Flavor-changing neutral current decays are highly suppressed in the standard model and their predicted properties could be significantly modified by new physics at the electroweak scale. We measure the branching fractions B(B -> K center dot(+)center dot(-))=(0.34 +/- 0.07 +/- 0.02)x10(-6), B(B -> K-*center dot(+)center dot(-))=(0.78(-0.17)(+0.19)+/- 0.11)x10(-6), the direct CP asymmetries of these decays, and the relative abundances of decays to electrons and muons. For two regions in center dot(+)center dot(-) mass, above and below m(J/psi), we measure partial branching fractions and the forward-backward angular asymmetry of the lepton pair. In these same regions we also measure the K-* longitudinal polarization in B -> K-*center dot(+)center dot(-) decays. Upper limits are obtained for the lepton-flavor-violating decays B -> Ke mu and B -> K(*)e mu. All measurements are consistent with standard model expectations.