Cosmology requires at least half of the baryons in the Universe to be in the intergalactic medium, much of which is believed to form hot coronae around galaxies. Star-forming galaxies must be accreting from their coronae. Hi observations of external galaxies show that they have Hi halos associated with star formation. These halos are naturally modelled as ensembles of clouds driven up by supernova bubbles. These models can fit the data successfully only if clouds exchange mass and momentum with the corona. As a cloud orbits, it is ablated and forms a turbulent wake where cold high-metallicity gas mixes with hot coronal gas causing the prompt cooling of the latter. As a consequence the total mass of Hi increases. This model has recently been used to model the Leiden-Argentina-Bonn survey of Galactic Hi. The values of the model’s parameters that are required to model NGC 891, NGC 2403 and our Galaxy show a remarkable degree of consistency, despite the very different natures of the two external galaxies and the dramatic difference in the nature of the data for our Galaxy and the external galaxies. The parameter values are also consistent with hydrodynamical simulations of the ablation of individual clouds. The model predicts that a galaxy that loses its cool-gas disc for instance through a major merger cannot reform it from its corona; it can return to steady star formation only if it can capture a large body of cool gas, for example by accreting a gas-rich dwarf. Thus the model explains how major mergers can make galaxies “red and dead.”