A quantitative description of the surface morphology evolution in thin film growing via 3D island mechanism is presented. The treatment is based on the calculation of the survival probability for any point on (or above) a substrate during growth process. The paraboloid growth model is considered. In this model, the lateral growth of an island occurs in a circle form via capture of migrating adatoms, while its vertical growth proceeds at constant velocity owing to direct impingement of deposited atoms. so that a steady (in time) and random (in space) surface relief consisting of paraboloid growth hillocks is developed eventually. For this surface relief, forming at paraboloid growth, the height-height autocorrelation function is derived for different hillock shape and different nucleation mode generating different hillock space distribution. It is found that the hillock shape strongly affects on the overall surface roughness and the hillock space distribution influences on both the autocorrelation function form and the rms roughness. The surface height distribution is asymmetric, non-Gaussian with negative skewness. The random rough surface of thin film with surely non-Gaussian height distribution is characterized by close-to-Gaussian height-height correlation function. (C) 2003 Elsevier Science B.V. All rights reserved.