Aluminium was anodised in H2SO4 solutions 0.25–1.53 M, temperatures 0–35 °C, times up to 90 min and voltage 25 V. Anodising was followed chronoamperometrically. The passing charge, consumed Al, formed oxide, transport numbers of oxygen anions in barrier layer and film thicknesses were determined. Films were examined to detect abnormal film growth, called burning. It was found that the current in Al anode is closely solely ionic, and the only processes occurring are those related with ionic charge transport and heat release and its abduction for which suitable equations were formulated relating many parameters. At each concentration, the temperatures, current densities and times up to which normal film growth occurs and above which stain-like mild, island-like intermediate, strong, strong-destructive and mixed burning appears were found. Burning emerges at lower concentrations, temperatures and times for thinner Al. Low concentrations and temperatures among thresholds where mild and next-kind burning first appear define windows of conditions where thick enough dark or black films grow. Peculiar chronoamperometric plot characterises each film growth type. Though other burning kinds can appear at each surface region or in the whole surface, strong and strong-destructive emerge only at the lower Al side around which the efficiency of solution stirring is highest. The mechanisms of normal and abnormal film growth were formulated showing that different processes and interacting variable parameters, some of which are noted for first time, regulate each film growth type. These can predict methods to avoid abnormal film growth.