  In a previous paper (arXiv:1011.1895), we showed that saturation models,
constrained by e+p HERA data on inclusive and diffractive cross-sections, are
in good agreement with p+p data at LHC in the soft sector. Particularly
impressive was the agreement of saturation models with the multiplicity
distribution as a function of $n_{\rm ch.}$. In this paper, we extend these
studies further and consider the agreement of these models with data on bulk
distributions in A+A collisions. We compare our results to data on central and
forward particle production in d+Au collisions at RHIC and make predictions for
inclusive distributions in p+Pb collisions at the LHC.
