Understanding and controlling nucleate pool boiling phenomena in zero gravity conditions is fundamental for space applications. An analytical model for the equilibrium radius reached by a bubble nucleated in sub-cooled conditions is established in this work and verified numerically. Indeed, direct numerical simulations of two phase flows conjugated with the heat conduction in the solid wall are carried out in order to verify and correct the analytical model. Fine grids, with cells size of the order of the micron, are manda- tory in order to capture the subtle equilibrium between condensation and evaporation that characterises stationary conditions. This has been possible thanks to the house made solver DIVA, validated for nucleate pool boiling simulations, and that permits to carry out parallel numerical simulations. Results show that the equilibrium radius of the bubble is a function of the thermal gradient, of the Jakob numbers associated with condensation and evaporation and of the apparent contact angle. The analysis of the thermal field is carried out and an interpretation of the physical processes that characterise the equilibrium is given. In addition, useful information on the heat transfer behaviour, reported in terms of Nu numbers, completes the work.