Cumulative particle production and percolation of strings

Calculations of the production rate of particles with $x>1$ in nuclear collisions due to the interaction of colour strings are presented. Momentum and colour sum rules are used to determine the fragmentation functions of fused strings. Mechanisms of the string interaction are considered with total and partial overlapping in the transverse plane. The results reveal strong dependence of the chosen mechanism. In the percolation scenario with partial overlapping the $x$-dependence of the production rates agrees well with the existing data. The magnitude of the rates for $\pi^+$ production is in agreement with experiment. However the rates for the protons are substantially below the data.