  Tunnel transport processes are considered in a square lattice of metallic
nanogranules embedded into insulating host to model tunnel conduction in real
metal/insulator granular layers. Based on a simple model with three possible
charging states ($\pm$, or 0) of a granule and three kinetic processes
(creation or recombination of a $\pm$ pair, and charge transfer) between
neighbor granules, the mean-field kinetic theory is developed. It describes the
interplay between charging energy and temperature and between the applied
electric field and the Coulomb fields by the non-compensated charge density.
The resulting charge and current distributions are found to be essentially
different in the free area (FA), between the metallic contacts, or in the
contact areas (CA), beneath those contacts. Thus, the steady state dc transport
is only compatible with zero charge density and ohmic resistivity in FA, but
charge accumulation and non-ohmic behavior are \emph{necessary} for conduction
over CA. The approximate analytic solutions are obtained for characteristic
regimes (low or high charge density) of such conduction. The comparison is done
with the measurement data on tunnel transport in related experimental systems.
