| Summary: | We perform amplitude analyses of the decays B[superscript 0]→K[superscript +]K[superscript -]K[subscript S][superscript 0], B[superscript +]→K[superscript +]K[superscript -]K[superscript +], and B[superscript +]→K[subscript S][superscript 0]K[subscript S][superscript 0]K[superscript +], and measure CP-violating parameters and partial branching fractions. The results are based on a data sample of approximately 470×10[superscript 6] BB̅ decays, collected with the BABAR detector at the PEP-II asymmetric-energy B factory at the SLAC National Accelerator Laboratory. For B[superscript +]→K[superscript +]K[superscript -]K[superscript +], we find a direct CP asymmetry in B[superscript +]→ϕ(1020)K[superscript +] of A[subscript CP]=(12.8±4.4±1.3)%, which differs from zero by 2.8σ. For B[superscript 0]→K[superscript +]K[superscript -]K[subscript S][superscript 0], we measure the CP-violating phase β[subscript eff](ϕ(1020)K[subscript S][superscript 0])=(21±6±2)°. For B[superscript +]→K[subscript S][superscript 0]K[subscript S][superscript 0]K[superscript +], we measure an overall direct CP asymmetry of A[subscript CP]=(4[subscript -5][superscript +4]±2)%. We also perform an angular-moment analysis of the three channels and determine that the f[subscript X](1500) state can be described well by the sum of the resonances f[subscript 0](1500), f[subscript 2][superscript ′](1525), and f[subscript 0](1710).
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