A systematic study of growing NaxCoO2 (x = 0.55-1.00) and NaxCoO2 center dot yH(2)O (x = 0.26-0.42, y = 1.3) single crystals has been performed to determine phase stability and the effect of hydration on the structural and magnetic properties of this system. Our experiments demonstrate that nearly pure alpha- (x = 0.90-1.00) and alpha'- (x = 0.75) phase of NaxCoO2 crystals could be obtained using the optical floating zone method, while other phases with lower sodium content of x < 0.70 (beta-phase with x = 0.55, 0.60 and gamma-phase with x = 0.65 and 0.70, respectively) are observed always to contain Na2O, Co3O4 and Na-poor phases. We give experimental evidence that the dependence of the superconducting transition temperature on Na content is much weaker than reported earlier. Implications of the Na effect for understanding of the structure, thermoelectricity, and superconducting phase diagram are discussed. (c) 2006 Elsevier B.V. All rights reserved.