  The recent experimental measurements on $pp$ collisions at $\sqrt{s}=5.02
\,\rm TeV$ have shown a very large abundance of heavy baryon production
corresponding to a ratio of $\Lambda_c/D^0 \sim 0.6$, about one order of
magnitude larger than what measured in $e^+e^-$, $ep$ collisions and even in
$pp$ collisions at LHC, but at forward rapidity. We apply for the first time to
$pp$ collisions a quark coalescence plus fragmentation approach developed for
$AA$ collisions, assuming the formation of Hot QCD matter at finite
temperature. An approach that has correctly predicted a $\Lambda_c/D \sim O(1)$
in AA collisions at RHIC energy. We calculate the heavy baryon/meson ratio and
the $p_T$ spectra of charmed hadrons with and without strangeness content:
$D^{0}$, $D_{s}$, $\Lambda_{c}^{+}$, $\Xi_c$ and $\Omega_c$ in $pp$ collisions
at top LHC energies, finding a satisfactory result for the measured
$\Lambda_{c}^{+}/D^0$ and the $\Xi_c/D^0$ without any specific tuning of
parameters to $pp$ collisions. At variance with other approaches a coalescence
approach predicts also a significant production of $\Omega_c$ such that
$\Omega_c/D^0 \sim O(10^{-1})$ .
