High-quality bulk MgB2 exhibits a structure of voids and agglomeration of crystals on different length scales. Because of this, the superconducting currents percolate between the voids in the ensuing structure. Magnetic measurements reveal that the superconducting currents circulate on at least three different length scales, of ∼1 μm, ∼10 μm, and whole of the sample (∼millimeter). Each of these screenings contributes to the measured irreversible magnetic moment (Δm). The analysis of the field dependence of Δm for samples of subsequently decreasing size showed that the critical current obtained using the simple critical state model is erroneous. This leads to the artifact of the sample size-dependent critical current density Jc and irreversibility field. Our data analysis enables the separation of the contribution of each of the screening currents to Δm. The field dependence of each of the currents follows a stretched exponential form. The currents flowing around whole of the sample give a dominant contribution to Δm in the intermediate fields (1 T<H<4 T at 20 K) and they can be used to obtain the value of Jc from critical state model, which corresponds to the transport Jc. The stretched exponential field dependence of these currents is similar to the one obtained for high-temperature superconductors, and it seems to be connected with the percolation of the currents.