Galaxy formation models typically assume that the size and rotation speed of galaxy discs are largely dictated by the mass, concentration and spin of their surrounding dark matter haloes. Equally important, however, is the fraction of baryons in the halo that collect into the central galaxy, as well as the net angular momentum that they are able to retain during its assembly process. We explore the latter using a set of four large cosmological N-body/gasdynamical simulations drawn from the OverWhelmingly Large Simulations project. These runs differ only in their implementation of feedback from supernovae (SNe). We find that, when expressed as fractions of their virial values, galaxy mass and net angular momentum are tightly correlated. Galaxy mass fractions, md=Mgal/Mvir, depend strongly on feedback but only weakly on halo mass, or spin over the halo mass range explored here (Mvir > 1011 h−1 M⊙). The angular momentum of a galaxy, expressed in units of that of its surrounding halo, jd=Jgal/Jvir, correlates with md in a manner that is insensitive to feedback and that deviates strongly from the simple jd=md assumption often adopted in semi-analytic models of galaxy formation. The md–jd correlation implies that, in a given halo, galaxy disc size is maximal when the central galaxy makes up a substantial fraction (∼20–30 per cent) of all baryons within the virial radius (i.e. md∼ 0.03–0.05). At z= 2, such systems may host gaseous discs with radial scalelengths as large as those reported for star-forming discs by the SINS survey, even in moderately massive haloes of average spin. Extended discs at z= 2 may thus signal the presence of systems where galaxy formation has been particularly efficient, rather than the existence of haloes with unusually high spin parameter.