High-multiplicity pp collisions exhibit features, traditionally associated with nuclear effects. Coherence motivates to treat high-multiplicity pp, pA and AA collisions on an equal footing. We rely on the phenomenological parametrization for mean multiplicities of light hadrons and J/psi, assuming their linear dependence on N_{coll} in pA collisions. The results of this approach underestimate the recently measured production rate of J/psi at very high hadronic multiplicities. The linear dependence of J/psi multiplicity on N_{coll} is subject to predicted nonlinear corrections, related to mutual boosting of the saturation scales in colliding dense parton clouds. A parameter-free calculation of the non-linear corrections allows to explain data for pT-integrated yield of J/psi at high hadronic multiplicities. Calculations are in a good accord with data binned in several pT-intervals as well. As was predicted, Upsilon and J/psi are equally suppressed at forward rapidities in pA collisions. Consequently, their fractional multiplicities at forward rapidities in pp collisions are equal as well, and their magnitude agrees with data.
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