Context : Galaxy formation in the current cosmological paradigm is a very complex process in which inflows , outflows , interactions and mergers are common events . These processes can redistribute the angular momentum content of baryons . Recent observational results suggest that disc formed conserving angular momentum while elliptical galaxies , albeit losing angular momentum , determine a correlation between the specific angular momentum of the galaxy and the stellar mass . These observations provide stringent constraints for galaxy formation models in a hierarchical clustering scenario . Aims : We aim to analyse the specific angular momentum content of the disc and bulge components as a function of virial mass , stellar mass and redshift . We also estimate the size of the simulated galaxies and confront them with observations . Methods : We use cosmological hydrodynamical simulations that include an effective , physically-motivated Supernova feedback which is able to regulate the star formation in haloes of different masses . We analyse the morphology and formation history of a sample of galaxies in a cosmological simulation by performing a bulge-disc decomposition of the analysed systems and their progenitors . We estimate the angular momentum content of the stellar and gaseous discs , stellar bulges and total baryons . Results : In agreement with recent observational findings , our simulated galaxies have disc and spheroid components whose specific angular momentum contents determine correlations with the stellar and dark matter masses with the same slope , although the spheroidal components are off-set by a fixed fraction . The average angular momentum efficiency for the simulated discs is \eta \sim 1 while bulges is \eta \sim 0.10 - 0.20 . For the simulated sample , the correlations found for the specific angular momentum content as a function of virial mass or stellar mass are found not to evolve significantly with redshift ( up to z \sim 2 ) . Both dynamical components seem to move along the correlations as they evolve . The total specific angular momentum of galaxies occupy different positions filling the gap between pure rotational-dominated and dispersion-dominated systems . The scaling relations derived from the simulated galaxies determine a similar relation with the virial radius , in agreement with recent observations . Conclusions :