  In this paper we demonstrate that the vigorously growing multiplicity
distributions measured by STAR and ALICE present a strong evidence in favor of
multigluon fusion mechanisms of the quarkonia production in CGC approach. We
analyze the contribution of 3-gluon fusion mechanism and demonstrate that it
gives a sizeable contribution to quarkonia yields, as well as predicts
correctly the multiplicity distributions for $J/\psi$ at RHIC and LHC. We also
make predictions for other quarkonia states, such as $\psi(2S)$ and
$\Upsilon(1S)$, and find that the multiplicity dependence of these states
should be comparable to similar dependence for $J/\psi$. Finally, we discuss an
experimental setup in which very strong multiplicity dependence could be
observed. This observation would be a strong evidence in favor of CGC approach.
