The branching fractions of the decay B+ -> p (p) over barK(+) for different intermediate states are measured using data, corresponding to an integrated luminosity of 1.0 fb(-1), collected by the LHCb experiment. The total branching fraction, its charmless component (M-p (p) over bar _ < 2.85 GeV/c(2)) and the branching fractions via the resonant c<(c)over bar> c states eta c(1S) and psi(2S) relative to the decay via a J/psi intermediate state are B(B+ -> p (p) over bar K+)(total)/B(B+ -> J/psi K+ -> p (p) over barK(+)) = 4.91 +/- 0.19 (stat) +/- 0.14 (syst), B(B+ -> p (p) over bar K+) M-P (p) over bar<2.85 GeV/(2)/B(B+ -> J/psi K+ -> p<(p)over bar>K+) = 2.02 +/- 0.10 (stat) +/- 0.08 (syst), B(B+ -> eta(c) (1S)K+ -> p<(pover bar>K+)/B(B+ -> J/psi K+ -> p (p) over barK(+)) =0.578 +/- 0.035 (stat) +/- 0.027 (syst), B(B+ -> psi(2S)K+ -> p (p) over barK(+) )/B(B+ -> J/psi K+ -> p (p) over barK(+)) = 0.080 +/- 0.012 (stat) +/- 0.009 (syst). Upper limits on the B+ branching fractions into the eta(c)(2S) meson and into the charmonium-like states X(3872) and X(3915) are also obtained.