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

Theory of carrier concentration-dependent electronic behavior in layered cobaltates