The distribution of current density in the quantum Hall effect can be probed by the channel-width dependence of the critical current. Both linear and sublinear dependence have been found in such experiments. We observe a crossover from linear to strong sublinear behavior, in the same samples, upon the increase of carrier density. This crossover suggests the existence of qualitatively different regimes of current distribution. The linear behavior is attributed to percolative transport through numerous, randomly distributed microscopic channels, due to strong density fluctuations within the sample. The sublinear regime, on the other hand, is associated with relatively better homogeneity, where the macroscopic polarization of the channel leads to a current distribution that is weighted towards the sample boundaries. Our conclusions may resolve the conflict between recently reported experiments.