The kinetics and mechanism of growth of porous anodic alumina films were studied during potentiostatic Al anodising at suitable ranges of H2SO4 concentrations, temperatures, anodic potentials, stirring rates, distances of Al from stirrer and times. Chronoamperometry, determination of various physical and structural features and kinetic parameters and proper novel models interrelating anions transport numbers with field strength in barrier layer enabled the formlulation of a novel theory interpreting the observed for first time extraordinary kinetic behaviour and the mechanisms of normal growth and abnormal growth where burning appears. It turned out thatkey parameter is mean barrier layer thickness defined by inherent thinning in the second transient stage and by thinning and thickening coming from continuous initiation and termination of some pores in this and quasi-steady state stage. In normal growth wholly and locally in Al surface chronoamperometric plots sequentially show low maximum at the boundary of two stages and then shallow minimum and high maximum in the last stage as the rates of barrier layer thinning and thickening are balanced at the extremes while the first prevails in transient stage and among the two last extremes. In abnormal growth the first two extremes merge in transient stage as thinning rate prevails endlessly and burning appears. It first occurs after certain conditions thresholds at position with highest local current density, as a rule around the lower Al side where stirring efficiency is also highest. New conditions and methods for high rates normal growth and desired properties of films are reliably predicted for first time, vital for Al anodising electrochemistry. (C) 2016 Elsevier B.V. All rights reserved.