Abstract: A study of the two-body decays B-+/- -> Xc (c) over barK +/-, where X-c (c) over bar refers to one charmonium state, is reported by the BABAR Collaboration using a data sample of 424 fb(-1). The absolute determination of branching fractions for these decays are significantly improved compared to previous BABAR measurements. Evidence is found for the decay B-+/- -> X(3872)K+ at the 3 sigma level. The absolute branching fraction B[B+ -> X(3872)K+] = [2.1 +/- 0.6(stat) +/- 0.3(syst)] x 10(-4) is measured for the first time. It follows that B[X(3872) -> J/psi pi(+)pi(-)] = (4.1 +/- 1.3)%, supporting the hypothesis of a molecular component for this resonance.