The branching fractions of the decay $B^{+} to p bar p K^{+}$ 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 $(M_{pbar p} <2.85 {GeV/}c^{2})$ and the branching fractions via the resonant $cbar c$ states $eta_{c}(1S)$ and $psi(2S)$ relative to the decay via a $J/psi$ intermediate state are {align*} frac{{mathcal B}(B^{+} to p bar p K^{+})_{total}}{{mathcal B}(B^{+} to J/psi K^{+} to p bar p K^{+})}=& , 4.91 pm 0.19 , {(rm stat)} pm 0.14 , {(rm syst)}, frac{{mathcal B}(B^{+} to p bar p K^{+})_{M_{pbar p} <2.85 {GeV/}c^{2}}}{{mathcal B}(B^{+} to J/psi K^{+} to p bar p K^{+})}=& , 2.02 pm 0.10 , {(rm stat)}pm 0.08 , {(rm syst)}, frac{{mathcal B} (B^{+} to eta_{c}(1S) K^{+} to p bar p K^{+})}{{mathcal B}(B^{+} to J/psi K^{+} to p bar p K^{+})} = & , 0.578 pm 0.035 , {(rm stat)} pm 0.027 , {(rm syst)}, frac{{mathcal B} (B^{+} to psi(2S) K^{+} to p bar p K^{+})}{{mathcal B}(B^{+} to J/psi K^{+} to p bar p K^{+})}=& , 0.080 pm 0.012 , {(rm stat)} pm 0.009 , {(rm syst)}. {align*} 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.