A general method for quantitative description of growth and morphology evolution in thin film growing via 3D island mechanism is presented. The method is based on the calculation of the survival probability for any point on (or above) a substrate. The growth law for different island growth mode (hemisphere and paraboloid) and condensation regime is derived in a self-consistent manner at all successive deposition stages, which shows growth acceleration at late stages due to island collisions. A temporal evolution of a lateral growth front perimeter that can be used for experimental determination of the growth law is also given. For surface relief, forming at paraboloid growth, the height-height autocorrelation function (ACF) is derived for different hillock shape and different nucleation mode generating different hillock space distribution. It is found that the hillock shape strongly affects the overall surface roughness and the hillock space distribution influences on both the ACF form and the rms roughness. For hemisphere growth surface morphology evolution during film growth is analyzed in terms of the rms surface roughness and the roughness coefficient and it is shown that both of them can be presented as a universal (independent of a growth regime) unimodal function of either coverage or film thickness with a maximum just prior to the completed film formation.