Gas evolving reactions are ubiquitous in the operation of electrochemical devices. Recent studies of individual gas bubbles on nanoelectrodes have resulted in unprecedented control and insights on their formation. The experiments, however, lack the spatial resolution to elucidate the molecular pathway of nucleation of nanobubbles and their stationary size and shape. Here we use molecular simulations with an algorithm that mimics the electrochemical formation of gas, to investigate the mechanisms of nucleation of gas bubbles on nanoelectrodes, and characterize their stationary states. The simulations reproduce the experimental currents in the induction and stationary stages, and indicate that surface nanobubbles nucleate through a classical mechanism. We identify three distinct regimes for bubble nucleation, depending on the binding free energy per area of bubble to the electrode, Delta gamma(bind). If Delta gamma(bind) is negative, the nucleation is heterogeneous and the nanobubble remains bound to the electrode, resulting in a low-current stationary state. For very negative Delta gamma, the bubble fully wets the electrode, forming a one-layer-thick micropancake that nucleates without supersaturation. On the other hand, when Delta gamma(bind) > 0 the nanobubble nucleates homogeneously close to the electrode, but never attaches to it. We conclude that all surface nanobubbles must nucleate heterogeneously. The simulations reveal that the size and contact angle of stationary nanobubbles increase with the reaction driving force, although their residual current is invariant. The myriad of driven nonequilibrium stationary states with the same rate of production of gas, but distinct bubble properties, suggests that these dissipative systems have attractors that control the stationary current.