Recent work in galaxy formation has enlightened the important role of baryonic physics to solve the main problems encountered by the standard theory at the galactic scale, such as the galaxy stellar mass function or the problem of missing satellites. The present work aims at investigating the role of the cold and dense molecular phase, which could be a gas reservoir in the outer galaxy discs, with low star-formation efficiency. By using hydrodynamical simulations, implementing the cooling to low temperatures, and including the molecular hydrogen component, several feedback efficiencies are studied, and results on the gas morphology and star formation are obtained. It is shown that molecular hydrogen allows some slow star formation (with gas depletion times of ∼5 Gyr) to occur in the outer parts of the discs. This dense and quiescent phase might be a way to store a significant fraction of dark baryons in a relatively long timescale in the complete baryonic cycle that connects the galaxy discs to hot gaseous haloes and to the cosmic filaments.