Abstract Measurements of the production cross sections of prompt D0, D+, D*+, D s + $$ {\textrm{D}}_{\textrm{s}}^{+} $$ , Λ c + $$ {\Lambda}_{\textrm{c}}^{+} $$ , and Ξ c + $$ {\Xi}_{\textrm{c}}^{+} $$ charm hadrons at midrapidity in proton-proton collisions at s $$ \sqrt{s} $$ = 13 TeV with the ALICE detector are presented. The D-meson cross sections as a function of transverse momentum (p T) are provided with improved precision and granularity. The ratios of p T-differential meson production cross sections based on this publication and on measurements at different rapidity and collision energy provide a constraint on gluon parton distribution functions at low values of Bjorken-x (10 −5–10 −4). The measurements of Λ c + $$ {\Lambda}_{\textrm{c}}^{+} $$ ( Ξ c + $$ {\Xi}_{\textrm{c}}^{+} $$ ) baryon production extend the measured p T intervals down to p T = 0(3) GeV/c. These measurements are used to determine the charm-quark fragmentation fractions and the c c ¯ $$ \textrm{c}\overline{\textrm{c}} $$ production cross section at midrapidity (|y| < 0.5) based on the sum of the cross sections of the weakly-decaying ground-state charm hadrons D0, D+, D s + $$ {\textrm{D}}_{\textrm{s}}^{+} $$ , Λ c + $$ {\Lambda}_{\textrm{c}}^{+} $$ , Ξ c 0 $$ {\Xi}_{\textrm{c}}^0 $$ and, for the first time, Ξ c + $$ {\Xi}_{\textrm{c}}^{+} $$ , and of the strongly-decaying J/ψ mesons. The first measurements of Ξ c + $$ {\Xi}_{\textrm{c}}^{+} $$ and Σ c 0 , + + $$ {\Sigma}_{\textrm{c}}^{0,++} $$ fragmentation fractions at midrapidity are also reported. A significantly larger fraction of charm quarks hadronising to baryons is found compared to e+e − and ep collisions. The c c ¯ $$ \textrm{c}\overline{\textrm{c}} $$ production cross section at midrapidity is found to be at the upper bound of state-of-the-art perturbative QCD calculations.