contained in gas-rich satellite galaxies because they can contribute at most 10 percent of the required gas mass (Kauffmann et al. 2010; Di Teodoro & Fraternali 2014, ). Likewise, high-velocity [[H]{}[<span style="font-variant:small-caps;">i</span> ]{}]{}clouds contribute 3-5 times less gas than required to sustain the Milky Way star formation (Richter 2012). A potentially more substantial source of fresh material is the cooling flow of low-metallicity, ionised gas in a galaxy’s halo (Shull et al. 2009). This may be related to the “fountain” gas which is driven to a height of a few kpc from the disc by star formation, and may trigger a gas inflow rate very close to the star formation rate (Fraternali et al. 2013). Recent theoretical studies suggest that the fountain driven gas naturally produces an outside-in shrinking galactic disk (Elmegreen et al. 2014), which is consistent with what is observed for nearby dwarf galaxies (Zhang et al. 2012). However, it does not explain the observed inside-out growth of more massive disk galaxies (J. Wang et al. 2011), or their chemical evolution (Spitoni et al. 2013), which have been both explained in terms of a cosmological radial gas accretion (Kauffmann 1996, Spitoni et al. 2013).

In the framework of 