  The central exclusive production of $\chi_{c}$ and $\chi_{b}$ at the LHC,
RHIC and Tevatron energies is analyzed, using the recent unintegrated parton
distribution (UGDs) functions available in the package TMDlib. Comparison with
data is performed, which tests the underlying assumptions basing the
theoretical approach and it can constrain the unintegrated gluon distribution
function at the small-$x$ region. Predictions for LHC energies using recent
UGDs based in CCFM formalism are provided. It is explored the underlying
uncertainties on this production as the choice for the unintegrated gluon
distribution and factorization scale is done. Moreover, based on the parton
saturation model for the gluon distribution, analytical expressions for the
rapidity distributions are proposed. The prompt production of $J/\psi+\gamma$
and $\Upsilon+\gamma$ is computed for the first time for LHC energies within
the very same formalism used for $\chi$ production.
