Measurement of branching fractions and rate asymmetries in the rare decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

In a sample of 471×106 BB̅ events collected with the BABAR detector at the PEP-II e+e- collider we study the rare decays B→K(*)l+l-, where l+l- is either e+e- or μ+μ-. We report results on partial branching fractions and isospin asymmetries in seven bins of dilepton mass-squared. We further present CP and lepton-flavor asymmetries for dilepton masses below and above the J/ψ resonance. We find no evidence for CP or lepton-flavor violation. The partial branching fractions and isospin asymmetries are consistent with the Standard Model predictions and with results from other experiments.