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We present measurements of the branching fractions of the decays B+-->eta'K+ and B0-->eta'K0. For B0-->eta(')K(0)(S) we also measure the time-dependent CP-violation parameters S eta'(K(0)(S)) and C eta'(K(0)(S)), and for B+-->eta'K+ the time-integrated charge asymmetry A(ch). The data sample corresponds to 88.9 x 10(6) BB pairs produced by e(+)e(-) annihilation at …