  Recently the unusual metallic state with a substantially non-uniform
distribution of a charge and mag\-ne\-tic density in CoO$_2$ planes was found
experimentally in the Na$_x$CoO$_2$ compound with $x>0.6$. We have investigated
an origin of such electron disproportionation in the lamellar sodium cobaltates
by calculating the ion states as a function of a strength of the electron
correlations in the $d$(Co)-shells within the GGA+U approximation for the
system with a realistic crystal structure. It was found that the nonuniformity
of spin and charge densities are induced by an ordering of the sodium cations
and enhanced correlations. Two important magnetic states of cobalt lattice
competing with each other at realistic values of the correlation parameter were
found~---~low spin hexagons (LS) and higher spin kagom\'e lattice (HS-KSL). In
the heterogeneous metallic HS-KSL phase magnetic Co ions form a kagom\'e
structure. In LS phase the kagom\'e pattern is decomposed into hexagons and Co
ions possess minimal values of their spin. Coexistence of these states could
explain the emergence of the disproportionation with the peculiar kagom\'e
structure experimentally revealed in previous studies of the cobaltates.
