  Determining the spatial distribution and intrinsic physical properties of
neutral hydrogen on cosmological scales is one of the key goals of
next-generation radio surveys. We use the EAGLE galaxy formation simulations to
assess the properties of damped Lyman-alpha absorbers (DLAs) that are
associated with galaxies and their underlying dark matter haloes between 0
$\leq$ z $\leq$ 2. We find that the covering fraction of DLAs increases at
higher redshift; a significant fraction of neutral atomic hydrogen (HI) resides
in the outskirts of galaxies with stellar mass greater than or equal to
10$^{10}$ M$_\odot$; and the covering fraction of DLAs in the circumgalactic
medium (CGM) is enhanced relative to that of the interstellar medium (ISM) with
increasing halo mass. Moreover, we find that the mean density of the HI in
galaxies increases with increasing stellar mass, while the DLAs in high- and
low-halo-mass systems have higher column densities than those in galaxies with
intermediate halo masses (~ 10$^{12}$ M$_\odot$ at z = 0). These high-impact
CGM DLAs in high-stellar-mass systems tend to be metal-poor, likely tracing
smooth accretion. Overall, our results point to the CGM playing an important
role in DLA studies at high redshift (z $\geq$ 1). However, their properties
are impacted both by numerical resolution and the detailed feedback
prescriptions employed in cosmological simulations, particularly that of AGN.
