One of the biggest questions in galaxy formation is how gas from the inter-galactic medium is accreting onto galaxies to fuel star formation. Numerical simulations predict that there is a large reservoir of gas in filamentary structures surrounding the galaxies. Until today it has proven to be extremely challenging to observe this intergalactic gas as most of it is ionised. To detect the gas in neutral hydrogen non-trivial observations are required to reach a brightness sensitivity that probes the column densities of Lyman Limit systems. I will present recent observations with the Australia Telescope Compact Array that confirm very faint HI features outside of galaxies, which were tentatively detected in previous studies. Some of these objects do not have obvious optical counterparts and could be the denser components of an underlying Cosmic Web.