  We calculate several differential distributions for exclusive double
diffractive $\chi_c(0^{++})$ production in proton-antiproton collisions at the
Tevatron and in proton-proton collisions at RHIC and LHC in terms of
unintegrated gluon distributions (UGDFs) within the $k_t$-factorisation
approach. The uncertainties of the Khoze-Martin-Ryskin approach are discussed
in detail. The $g^* g^* \to \chi_c(0^{++})$ transition vertex is calculated as
a function of gluon virtualities applying the standard pNRQCD technique. The
off-shell effects are discussed and quantified. They lead to a reduction of the
cross section by a factor 2--5, depending on the position in the phase space
and UGDFs. Different models of UGDFs are used and the results are shown and
discussed. The cross section for diffractive component depends strongly on
UGDFs. We calculate also the differential distributions for the $\gamma^*
\gamma^* \to \chi_c(0^{++})$ fusion mechanism. The integrated cross section for
photon-photon fusion is much smaller than that of diffractive origin. The two
components have very different dependence on momentum transfers $t_1, t_2$ in
the nucleon lines as well as azimuthal-angle correlations between both outgoing
nucleons.
