Process of bromate reduction from aqueous acidic medium at (hemi) spherical microelectrode under steady-state conditions has been analyzed theoretically. Since bromate anion is non-electroactive within the potential range under consideration its transformation is based on the electroreduction of bromine which is present in bulk solution in small (even trace) amounts while the bromine reduction product, bromide anion, reacts irreversibly in acidic conditions with bromate anion, with regeneration of bromine, thus forming a redox mediator cycle. Similar to our previous studies of this process at rotating disk electrode it has been shown that this process possesses autocatalytic features, which may under certain conditions leads to considerable accumulation of the redox-couple components, Br-2 and Br-, near the electrode surface. As a result the rate of the bromate transformation by the catalytic cycle becomes so rapid that the rate of the whole process is controlled by the bromate transport from the bulk solution to the kinetic layer near the electrode surface, i.e. the current becomes comparable to a very high BrO3- diffusion limited one. For such an autocatalytic passage of the process the radius of the microelectrode has to exceed a critical value which depends on the solution composition. This peculiarity of the system leads to the anomalous dependence of the maximal current density of the bromate reaction on the electrode size: if the electrode radius is under its critical value the current density is very small since it is determined by the discharge of bromine species from the bulk solution, with no significant transformation of bromate. On the contrary, for larger electrodes the autocatalytic EC '' mechanism becomes efficient and the passing current density can exceed the bromate diffusion limited one, i.e. it is a very strong one. The theory also predicts a complicated dependence of the maximal current on the bulk solution concentrations of bromate and protons. (C) 2017 Elsevier Ltd. All rights reserved.