  We report a systematic angle-resolved photoemission study on Na$_x$CoO$_2$
for a wide range of Na concentrations ($0.3 \leq x \leq 0.72$). In all the
metallic samples at different $x$, we observed (i) only a single hole-like
Fermi surface centered around $\Gamma$ and (ii) its area changes with $x$
according to the Luttinger theorem. We also observed a surface state that
exhibits a larger Fermi surface area. The $e_g^\prime$ band and the associated
small Fermi surface pockets near the $K$ points predicted by band calculations
are found to ``sink'' below the Fermi energy in a manner almost independent of
the doping and temperature.
