The Australian Square Kilometre Array Pathfinder (ASKAP) will revolutionize our knowledge of gas-rich galaxies in the Universe. Here we present predictions for two proposed extragalactic ASKAP neutral hydrogen (H i) emission-line surveys, based on semi-analytic models applied to cosmological N-body simulations. The ASKAP H i All-Sky Survey, known as Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY), is a shallow 3 π survey
(z = 0–0.26) which will probe the mass and dynamics of over 6 × 105 galaxies. A much deeper small-area H i survey, called Deep Investigation of Neutral Gas Origins (DINGO), aims to trace the evolution of H i from z = 0 to 0.43, a cosmological volume of 4 × 107 Mpc3, detecting potentially 105 galaxies. The high-sensitivity 30 antenna ASKAP core (diameter ∼2 km) will provide an angular resolution of 30 arcsec (at z = 0). Our simulations show that the majority of galaxies detected in WALLABY (87.5 per cent) will be resolved. About 5000 galaxies will be well resolved, i.e. more than five beams (2.5 arcmin) across the major axis, enabling kinematic studies of their gaseous discs. This number would rise to 1.6 × 105 galaxies if all 36 ASKAP antennas could be used; the additional six antennas provide baselines up to 6 km, resulting in an angular resolution of 10 arcsec. For DINGO this increased resolution is highly desirable to minimize source confusion, reducing confusion rates from a maximum of 10 per cent of sources at the survey edge to 3 per cent. We estimate that the sources detected by WALLABY and DINGO will span four orders of magnitude in total halo mass (from 1011 to 1015 M⊙) and nearly seven orders of magnitude in stellar mass (from 105 to 1012 M⊙), allowing us to investigate the process of galaxy formation across the last four billion years.