  In this paper we analyze in detail the production of the $\chi_{c}$ and
$\chi_{b}$ mesons in $pp$ collisions. Using the color dipole framework, we
estimated the cross-sections in the kinematics of ongoing and forthcoming
experiments, and found that our estimates are in reasonable agreement with
currently available experimental data. We also analyzed the dependence on
multiplicity of co-produced hadrons and found that it is significantly milder
than that of $S$-wave quarkonia. We expect that the experimental confirmation
of this result could constitute an important test of our understanding of
multiplicity enhancement mechanisms in the production of different quarkonia
states.
