MHONGOOSE is a deep survey of the neutral hydrogen distribution in a representative sample of 30 nearby disk and dwarf galaxies with HI masses from 10^6 to ~10^{11} M_sun, and luminosities from M_R ~ -12 to M_R ~ -22. The sample is selected to uniformly cover the available range in log(M_HI). Our extremely deep observations, down to HI column density limits of well below 10^{18} cm^{-2} - or a few hundred times fainter than the typical HI disks in galaxies - will directly detect the effects of cold accretion from the intergalactic medium and the links with the cosmic web. These observations will be the first ever to probe the very low-column density neutral gas in galaxies at these high resolutions. Combination with data at other wavelengths, most of it already available, will enable accurate modelling of the properties and evolution of the mass components in these galaxies and link these with the effects of environment, dark matter distribution, and other fundamental properties such as halo mass and angular momentum. MHONGOOSE can already start addressing some of the SKA-1 science goals and will provide a comprehensive inventory of the processes driving the transformation and evolution of galaxies in the nearby universe at high resolution and over 5 orders of magnitude in column density. It will be a Nearby Galaxies Legacy Survey that will be unsurpassed until the advent of the SKA, and can serve as a highly visible, lasting statement of MeerKATs capabilities.
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