A quantitative theory is developed for better understanding of the potentiostatic growth of passivating films on metals following a previously proposed general treatment for voltammetric and galvanostatic transients. The theory is based, in this case, on an ohmic model for the current/overpotential relation inside the film and a Tafel relation for current/overpotential at the metal/film interface. The equations are applied to the potentiostatic growth of the passivating film on Zn in 0.3 M H3BO3 plus 0.15 M Na2B4O7 solution. It is shown that the initial charge, after electrode polishing and before potentiostatic growth, can be disregarded. It is then observed that, during potentiostatic growth, the film ionic specific resistivity decays, passes through a minimum value, arid then increases, giving rise to an aged film. The time for the occurrence of this last increase is proposed to be called "aging time." As a result, there is the appearance in the potentiostatic experiments of a maximum charge for film formation, which depends on the growth potential. This maximum charge presents, with the increase of the growth potential, a maximum followed by subsequent increase. As a consequence, it is proposed that the results can be interpreted through the existence of two kinds of films present, each appearing in two different potential regions. Finally, a general explanation is proposed for the evolution of the ionic specific resistivity in terms of the existence of defect injection at the metal/film (interstitial cations) and film/solution (cation vacancies) interfaces, the migration of the defects and their recombination inside the film.