The multiple hadron production in high energy collisions is studied in the framework of the simple model which enables to take into account the effects of a color quark-gluon string fusion [1, 2]. The model with a lattice in transverse plain is used for the calculation of the correlation coefficients between multiplicities and between the average transverse momentum and the multiplicity in realistic case of non-uniform string distribution in transverse plane. The asymptotes of the correlation coefficients at large string density are found. It is shown that the received asymptotes in case of uniform string dis-tribution in transverse plane are transformed into the ones obtained in papers [2-4].