  We have studied the superconducting phase diagram of \NaH\space as a function
of electronic doping, characterizing our samples both in terms of Na content
$x$ and the Co valence state. Our findings are consistent with a recent report
that intercalation of \oxp\space ions into Na$_{x}$CoO$_{2}$, together with
water, act as an additional dopant indicating that Na sub-stochiometry alone
does not control the electronic doping of these materials. We find a
superconducting phase diagram where optimal \Tc\space is achieved through a Co
valence range of 3.24 - 3.35, while \Tc\space decreases for materials with a
higher Co valence. The critical role of dimensionality in achieving
superconductivity is highlighted by similarly doped non-superconducting
anhydrous samples, differing from the superconducting hydrate only in
inter-layer spacing. The increase of the interlayer separation between
CoO$_{2}$ sheets as Co valence is varied into the optimal \Tc\space region is
further evidence for this criticality.
