  A natural explanation for the carrier concentration-dependent electronic
behavior in the layered cobaltates emerges within correlated-electron
Hamiltonians with finite on-site and significant nearest neighbor hole-hole
Coulomb repulsions. The nearest neighbor repulsion decreases hole
double-occupancy below hole density 1/3, but increases the same at higher hole
densities. Our conclusion is valid for both single-band and three-band extended
Hubbard Hamiltonians, and sheds light on concentration-dependent $e_g^\prime$
hole occupancy within the latter.
