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 $(M_{p\bar p} <2.85 {GeV/}c^{2})$ and the branching fractions via the resonant $c\bar c$ states $��_{c}(1S)$ and $��(2S)$ relative to the decay via a $J/��$ intermediate state are {align*} \frac{{\mathcal B}(B^{+} \to p \bar p K^{+})_{total}}{{\mathcal B}(B^{+} \to J/��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_{p\bar p} <2.85 {GeV/}c^{2}}}{{\mathcal B}(B^{+} \to J/��K^{+} \to p \bar p K^{+})}=& \, 2.02 \pm 0.10 \, {(\rm stat)}\pm 0.08 \, {(\rm syst)}, \frac{{\mathcal B} (B^{+} \to ��_{c}(1S) K^{+} \to p \bar p K^{+})}{{\mathcal B}(B^{+} \to J/��K^{+} \to p \bar p K^{+})} = & \, 0.578 \pm 0.035 \, {(\rm stat)} \pm 0.027 \, {(\rm syst)}, \frac{{\mathcal B} (B^{+} \to ��(2S) K^{+} \to p \bar p K^{+})}{{\mathcal B}(B^{+} \to J/��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 $��_{c}(2S)$ meson and into the charmonium-like states X(3872) and X(3915) are also obtained.

14 pages, 5 figures