We study the population of galactic discs expected in current hierarchical clustering models for structure formation. A rotationally supported disc with exponential surface density profile is assumed to form with a mass and angular momentum which are fixed fractions of those of its surrounding dark halo. We assume that haloes respond adiabatically to disc formation, and that only stable discs can correspond to real systems. With these assumptions the predicted population can match both present-day discs and the damped Ly alpha absorbers in QSO spectra. Good agreement is found provided that: (i) the masses of discs are a few per cent of those of their haloes; (ii) the specific angular momenta of discs are similar to those of their haloes; (iii) present-day discs were assembled recently (at z less than or equal to 1). In particular, the observed scatter in the size-rotation velocity plane is reproduced, as are the slope and scatter of the Tully-Fisher (TF) relation. The zero-point of the TF relation is matched for a stellar mass-to-light ratio of 1 to 2 h in the I-band, consistent with observational values derived from disc dynamics. High-redshift discs are predicted to be small and dense, and could plausibly merge together to form the observed population of elliptical galaxies. In many (but not all) currently popular cosmogonies, discs with rotation velocities exceeding 200 kms(-1) can account for a third or more of the observed damped Ly alpha systems at Z similar to 2.5. Half of the lines of sight to such systems are predicted to intersect the absorber at r greater than or similar to 3 k(-1) kpc and about 10 per cent at r > 10 h(-1) kpc. The cross-section for absorption is strongly weighted towards discs with large angular momentum and therefore large size for their mass. The galaxy population associated with damped absorbers should thus be biased towards low surface brightness systems.
