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The soft processes in pp, pA and AA collisions are considered in the Monte Carlo model with color string formation and fusion. The elementary nucleon collisions in the model are performed on the partonic level without usual assumptions of Glauber picture. The particle production is described in string model taking into account the interaction of strings in transverse plane in the approach of string fusion. Energy dependence of total inelastic cross section and mean charged multiplicity in pp collisions and recent p-Pb data on multiplicity at 5.02 TeV are used for the parameters turning. The comparison with experiment of the dependence of multiplicity per participant on the centrality in PbPb collisions at 2.76 TeV shows that good agreement is obtained only when the string fusion effects are present with the radius of string 0.2-0.3 fm. The rapidity distribution of multiplicity in PbPb collisions is calculated and compared with experimental data.

Monte Carlo model for pp, pA and AA collisions at high energy: parameters tuning and results