A thermodynamic analysis of the carbon nucleation on the metal surface was performed. From the consideration of the catalytic mechanisms of carbon deposit formation on the metal surface we concluded that majority of these mechanisms include some common steps. The most important of them is the step of nucleation of carbon deposit on the metal surface. The master equation for the dependence of critical radius of the nucleus on reaction parameters was obtained. This equation demonstrates that a variation of the reaction parameters, such as the temperature, the nature of metal catalyst and the degree of supersaturation of the metal-carbon solution, can lead to the formation of different carbon deposits, such as filamentous carbon, multi-wall nanotubes (MWNT) or single-wall nanotubes (SWNT). The analysis performed allows us to conclude that for selective production of SWNT the nucleation must proceed at high temperature on the surface of liquid metal particles (Fe, Co, Ni). For solid metal particles (Mo) a high degree of supersaturation with carbon is also required.