  A transport current distribution over a wide superconducting sheet is shown
to strongly change in a presence of bulk magnetic screens of a soft magnet with
a high permeability. Depending on the geometry, the effect may drastically
suppress or protect the Meissner state of the sheet through the enhancement or
suppression of the edge barrier critical current. The total transport current
in the magnetically screened Meissner state is expected to compete with the
critical current of the flux-filled sheet only for samples whose critical
current is initially essentially controlled by the edge barrier effect.
