Aluminium anodization in sulfuric acid at constant anodic potential was studied. The current density increased significantly in the second transient stage and gave successive extremes in the next quasi-steady state stage. The electrolysis voltage alike varied around the 25 V self-ordering regime. The porous anodic alumina films developed at strongly variable rate. Field emission scanning electron microscopy (FESEM) showed that the mean cell width, interpore spacing about 2.5 nm V⁻¹ and surface density of pores change in both stages. The first two parameters increase and the third decreases with the current density in the second transient stage. However, in the quasi-steady state, the first two vary inversely and the third similarly to current density. Concurrently, incessant termination/generation of pores occur. Pores that ceased growing, pores branching inwards and dendritic/serrated ones appear and their order changes. Structure change results from pores’ termination/generation during both stages and intrinsic thinning of the barrier layer during the first. Pores’ order improves when their termination rate exceeds generation one. It is maximized when these rates are low and balanced. Current density, nanostructure, self-ordering and incessant termination/generation of pores are strongly interdependent key factors of film growth.