We report a study of the decays B -> D_s1(2536)+ anti-D(*), where anti-D(*) is anti-D0, D- or D*-, using a sample of 657 x 10^6 B anti-B pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. The branching fractions of the decays B+ -> D_s1(2536)+ anti-D0, B0 -> D_s1(2536)+ D- and B0 -> D_s1(2536)+ D*- multiplied by that of D_s1(2536)+ -> (D*0K+ + D*+K0) are found to be (3.97+-0.85+-0.56) x 10^-4, (2.75+-0.62+-0.36) x 10^-4 and (5.01+-1.21+-0.70) x 10^-4, respectively.
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