Recently, we have proposed a simple kinetic model for layer epitaxial growth, which combines the rate equations approach and a feeding zone that allows accounting for the interlayer adatoms diffusion. With this model it has clearly been demonstrated how with decreasing surface adatom diffusivity and/or increasing the repulsive Ehrlich-Schwoebel (ES) barrier height growth, mode crosses over from atomically smooth layer-by-layer growth to a smooth multilayer growth and finally to a rough 3D growth, and corresponding 'phase diagram' of the growth mode in parametric space has been constructed. In this paper the role of the growing island collisions in the epitaxial growth is analyzed. To that end the comparative studies of the growth kinetics and morphology evolution in two extreme cases of the island collision process behaviour: impingement and coalescence are performed by numerical integration of the rate equations. It is shown that the character of the island collision process weakly affects on the location of demarcating lines in the phase diagram of the growth mode, which is determined by the growth parameters characterizing the surface adatoms diffusivity (mu) and the ES barrier (omega). It is found that in addition to these growth parameters, there exists important internal parameter, the critical coverage for the next layer nucleation, its magnitude uniquely determines the onset of a growth mode transition irrespective of p, and w thus remaining constant along a demarcating line. The growing island collisions significantly influence on the nucleation kinetics in successive layers and its scaling with growth parameters w and w and corresponding scaling exponents are determined.