We present a new kinetic model for molecular beam epitaxial growth on a singular surface which combines the modified rate equations approach with a concept of a feeding zone. The model involves irreversible nucleation, growth and coalescence of 2D islands in each layer and consists of an infinite set of coupled differential equations for adatom and 2D island densities and coverage in successive growing layers. It is shown that in the complete condensation regime and in the absence of step edge barriers, the homoepitaxial growth mode is fully determined by a single dimensionless parameter which is proportional to the ratio of the surface diffusion coefficient and the deposition flux. With decreasing this parameter, the growth mechanism crosses over from smooth 2D layer-by-layer growth to rough multilayer growth and eventually to very rough Poisson random deposition growth with time-divergent rms roughness. The extension of the model to the case of the heteroepitaxy by introducing different diffusion coefficients in the first and the next layers is presented as well.