We use the catalogue of 4315 extragalactic H i 21‐cm emission‐line detections from the H i Parkes All Sky Survey (HIPASS) to calculate the most accurate measurement of the H i mass function (HIMF) of galaxies to date. The completeness of the HIPASS sample is well characterized, which enables an accurate calculation of space densities. The HIMF is fitted with a Schechter function with parameters α=−1.37 ± 0.03 ± 0.05, log (M* H I/M⊙) = 9.80 ± 0.03 ± 0.03 h−275, and θ*= (6.0 ± 0.8 ± 0.6) × 10−3 h375 Mpc−3 dex−1 (random and systematic uncertainties at 68 per cent confidence limit), in good agreement with calculations based on the HIPASS Bright Galaxy Catalogue, which is a complete, but smaller, sub‐sample of galaxies. The cosmological mass density of H i in the local Universe is found to be ΩH i= (3.5 ± 0.4 ± 0.4) × 10−4 h−175. This large homogeneous sample allows us to test whether the shape of the HIMF depends on local galaxy density. We find tentative evidence for environmental effects in the sense that the HIMF becomes steeper toward higher density regions, ranging from α≈−1.2 in the lowest density environments to α≈−1.5 in the highest density environments probed by this blind H i survey. This effect appears stronger when densities are measured on larger scales.

The H I Parkes All-Sky Survey (HIPASS) catalogue forms the largest uniform catalogue of H I sources compiled to date, with 4315 sources identified purely by their H I content. The catalogue data comprise the southern region δ < + 2 • of HIPASS, the first blind H I survey to cover the entire southern sky. The rms noise for this survey is 13 mJy beam −1 and the velocity range is −1280 to 12 700 km s −1 . Data search, verification and parametrization methods are discussed along with a description of measured quantities. Full catalogue data are made available to the astronomical community including positions, velocities, velocity widths, integrated fluxes and peak flux densities. Also available are on-sky moment maps, position-velocity moment maps and spectra of catalogue sources. A number of local large-scale features are observed in the space distribution of sources, including the super-Galactic plane and the Local Void. Notably, large-scale structure is seen at low Galactic latitudes, a region normally obscured at optical wavelengths.

A comprehensive analysis of 355 high‐quality Westerbork Synthesis Radio Telescope (WSRT) H i 21‐cm line maps of nearby galaxies shows that the properties and incident rate of damped Lyman α absorption systems (DLAs) observed in the spectra of high‐redshift QSOs are in good agreement with DLAs originating in gas discs of galaxies like those in the z≈ 0 population. Comparison of low‐z DLA statistics with the H i incidence rate and column density distribution f(NH i) for the local galaxy sample shows no evidence for evolution in the integral ‘cross‐section density’〈nσ〉=l−1 (l= mean free path between absorbers) below z≈ 1.5, implying that there is no need for a hidden population of galaxies or H i clouds to contribute significantly to the DLA cross‐section. Compared with z≈ 4, our data indicate evolution of a factor of 2 in the comoving density along a line of sight. We find that dN/dz(z= 0) = 0.045 ± 0.006. The idea that the local galaxy population can explain the DLAs is further strengthened by comparing the properties of DLAs and DLA galaxies with the expectations based on our analysis of local galaxies. The distribution of luminosities of DLA host galaxies, and of impact parameters between QSOs and the centres of DLA galaxies, is in good agreement with what is expected from local galaxies. Approximately 87 per cent of low‐z DLA galaxies are expected to be fainter than L*, and 37 per cent have impact parameters less than 1 arcsec at z= 0.5. The analysis shows that some host galaxies with very low impact parameters and low luminosities are expected to be missed in optical follow‐up surveys. The well‐known metallicity–luminosity relation in galaxies, in combination with metallicity gradients in galaxy discs, causes the expected median metallicity of low‐z DLAs to be low (∼1/7 solar), which is also in good agreement with observations of low‐z DLAs. We find that f(NH i) can be fitted satisfactorily with a gamma distribution, a single power law is not a good fit at the highest column densities NH i > 1021 cm−2. The vast majority (≈81 per cent) of the H i gas in the local Universe resides in column densities above the classical DLA limit (NH i > 2 × 1020 cm−2), with NH i∼ 1021 cm−2 dominating the cosmic H i mass density.

Many of the results in modern astrophysics rest on the notion that the Initial Mass Function (IMF) is universal. Our observations of a sample of H I selected galaxies in the light of Hα and the far-ultraviolet (FUV) challenge this result. The extinction corrected flux ratio F Hα / f FUV from these two tracers of star formation shows strong correlations with the surface-brightness in Hα and the R band: Low Surface Brightness (LSB) galaxies have lower F Hα / f FUV ratios compared to High Surface Brightness (HSB) galaxies as well as compared to expectations from equilibrium models of constant star formation rate (SFR) using commonly favored IMF parameters. Weaker but significant correlations of F Hα / f FUV with luminosity, rotational velocity and dynamical mass are found as well as a systematic trend with morphology. The correlated variations of F Hα / f FUV with other global parameters are thus part of the larger family of galaxy scaling relations. The F Hα / f FUV correlations can not be due to residual extinction correction errors, while systematic variations in the star formation history can not explain the trends with both Hα and R surface brightness nor with other global properties. The possibility that LSB galaxies have a higher escape fraction of ionizing photons seems inconsistent with their high gas fraction, and observations of color-magnitude diagrams of a few systems which indicate a real deficit of O stars. The most plausible explanation for the correlations is the systematic variations of the upper mass limit M u and/or the slope γ which define the upper end of the IMF. We outline a scenario of pressure driving the correlations by setting the efficiency of the formation of the dense star clusters where the highest mass stars preferentially form. Our results imply that the star formation rate measured in a galaxy is highly sensitive to the tracer used in the measurement. A non-universal IMF would also call into question interpretation of metal abundance patterns in dwarf galaxies as well star formation histories derived from color magnitude diagrams.