Theory of the convective-diffusion transport for the steady-state electroreduction of bromate-anion at rotating disk electrode has been developed for the first time for the compositions of the bulk solution where the bromate concentration is much higher than the proton one. Because of the non-electroactivity of the bromate anions and protons the process proceeds via a redox cycle composed of the electrochemical reduction of bromine (always present in acidic bromate solutions) to bromide and of the comproportionation reaction between bromate, bromide and protons regenerating bromine species. The autocatalytic feature of the cycle can lead under certain conditions on the convection intensity to very strong accumulation of the redox-couple components, bromine and bromide, in the kinetic layer of the solution near the electrode surface, resulting in a very high rate of the overall process, which is controlled by transport of principal components of the bulk solution, namely by that of protons for systems with bromate excess. Theoretical description of such a situation is based on transport equations for all components of the system taking into account of both the convective and diffusional contributions to their fluxes, the bromate concentration being approximately considered as constant across the diffusion layer. Analytical formulas for the concentration distributions have been derived for all current densities that can pass through the RDE system for any rotation frequency. Principal results of this analysis for the bromate excess in the bulk solution are similar to those obtained within the framework of the previous approaches, in particular existence of an "anomalous frequency range" where the maximal current (for a fixed rotation frequency) rises drastically if the rotation frequency (i.e. the solution agitation intensity) decreases, as well as approach of the maximal current for the lower frequency range to the one limited by the convective-diffusion transport of protons. At the same time quantitative predictions of this novel theory and of conventional Nernst model of a stagnant layer has shown significant differences among them that cannot be avoided for any choice of the diffusion layer thickness. On the contrary, the recently proposed theoretical approach of the "Generalized Nernst Layer" model has turned out to be able to reproduce adequately both the concentration distributions inside the kinetic layer (in particular, the values of the concentrations at the electrode surface) for any passing current, as well as the dependence of the maximal current density on the disk rotation frequency (including the frequency ranges of the anomalous behavior and of very strong currents). As it has been expected intuitively, no model replacing the convective-diffusion transport outside the (thin) kinetic layer by a convection-free layer is able to describe properly the concentration profiles there. (C) 2017 Elsevier Ltd. All rights reserved.