The evolution of surface morphology during the growth of N-polar (000 (1) over bar) GaN under N-rich conditions is studied by kinetic Monte Carlo (kMC) simulations for two substrates miscuts 2 degrees and 4 degrees. The results are compared with experimentally observed surface morphologies of (000 (1) over bar) GaN layers grown by plasma assisted molecular beam epitaxy. The proposed kMC two-component model of GaN(000 (1) over bar) surface where both types of atoms, nitrogen and gallium, attach to the surface and diffuse independently shows that at relatively high rates of the step flow (miscut angle <2 degrees) the low mobility of gallium adatoms causes surface instabilities and leads to experimentally observed roughening while for low rates of the step flow (miscut 4 degrees), smooth surface can be obtained. In the presence of almost immobile nitrogen atoms under N-rich conditions crystal growth is realized by the process of two-dimensional island nucleation and coalescence. Larger crystal miscut, lower growth rate or higher temperature results in similar effect of the surface smoothening. We show that the surface also smoothens for the growth conditions with very high N-excess. In the presence of large number of nitrogen atoms the mobility of gallium atoms changes locally thus providing easier coalescence of separated island. (C) 2016 Elsevier B.V. All rights reserved.