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The total charm-quark production cross section per unit of rapidity dσ(cc)/dy, and the fragmentation fractions of charm quarks to different charm-hadron species f(c → hc), are measured for the first time in p–Pb collisions at √sNN = 5.02 TeV at midrapidity (−0.96 < y < 0.04 in the centre-ofmass frame) using data collected by ALICE at the CERN LHC. The results are obtained based on all the available measurements of prompt production of ground-state charm-hadron species: D0, D+,D+s, and J/ψ mesons, and Λ+cand Ξ0cbaryons. The resulting cross section is dσ(cc)/dy = 219.6±6.3 (stat.)+10.5−11.8(syst.)+7.6−2.9(extr.)±5.4 (BR)±4.6 (lumi.)±19.5 (rapidity shape) +15.0 (Ω0c) mb, which is consistent with a binary scaling of pQCD calculations from pp ollisions. The measured fragmentation fractions are compatible with those measured in pp collisions at √s = 5.02 and 13 TeV, showing an increase in the relative production rates of charm baryons with respect to charm mesons in pp and p–Pb collisions compared with e+e − and e−p collisions. The pT-integrated nuclear modification factor of charm quarks, RpPb(cc) = 0.91±0.04 (stat.) +0.08 −0.09 (syst.) +0.04 −0.03 (extr.)±0.03 (lumi.), is found to be consistent with unity and with theoretical predictions including nuclear modifications of the parton distribution functions.