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 Lyα 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 ≤ 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 km s−1 can account for a third or more of the observed damped Lyα systems at z ∼ 2.5. Half of the lines of sight to such systems are predicted to intersect the absorber at r ≳ 3 h−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.

In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for groundbased detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year (∼ 1 yr −1 ) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as ∼ 80 yr −1 . These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be ∼ 30 per cent for the aLIGO survey and ∼ 6 per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems (∼ 90 per cent) will have time delays less than ∼ 1 month, which will be far shorter than survey durations.