Field dependence of irreversible magnetic moment ∆m was obtained from magnetic hysteresis loops for a number of bulk MgB 2 superconductors. The field dependence of ∆m exhibits inflections at two characteristic fields, H t and H i (H t < H i ). These two fields increase linearly with the logarithm of the sample size, each extrapolating to zero at a different characteristic sample size. Magneto-optical, optical and scanning electron microscopic examinations show that these extrapolated sample sizes match the sizes of the main microscopic features of the samples. The inflection at H t and the sample size dependence of ∆m and H t are associated with voids scattered through the samples, which are observed for all bulk MgB 2 samples. The voids encircle cells of MgB 2 material of tens of micrometers in size. The cells are connected by narrow bridges. The superconducting currents screening the whole of the sample have to cross these bridges and they are concentrated in them. This promotes additional superconducting screening around the cells, where the current density would otherwise be smaller than the critical current density J c . The field dependence of the currents pertinent to each of the screenings follows the stretched exponential law. However, these two screening currents decrease with H with a different rate, and H t is a field of the transition from the dominance of one of the currents in ∆m to the other. The screening that gives predominant contribution to ∆m for H < H t is confined to inside the cells, circulating on ~10 µm-scale. For H t < H < H i , the dominant screening currents circulate the whole of the sample, percolating through the bridges. If J c is calculated from the critical state model assuming only the screening around the whole of the sample, erroneous value of J c and its functional dependence on the field are obtained. This also leads to an artifact of the sample size-dependent J c . However, because these two stretched exponential contributions decrease with H with a different rate, they can be separated for most of the samples. The magnetically obtained J c for H t < H < H i is defined by the screening currents percolating around the whole of the sample, and it is in good agreement with the transport J c . There is also a third tier of superconducting screening on a micrometer scale, inside the cells. It is associated with clusters of superconducting crystals that make up the cells. However, its contribution to ∆m is negligible for H < H i , which are the fields of technological interest.