  We compare the mass and internal distribution of atomic hydrogen (HI) in 2200
present-day central galaxies with M_star > 10^10 M_Sun from the 100 Mpc EAGLE
Reference simulation to observational data. Atomic hydrogen fractions are
corrected for self-shielding using a fitting formula from radiative transfer
simulations and for the presence of molecular hydrogen using an empirical or a
theoretical prescription from the literature. The resulting neutral hydrogen
fractions, M_(HI+H2)/M_star, agree with observations to better than 0.1 dex for
galaxies with M_star between 10^10 and 10^11 M_Sun. Our fiducial, empirical H2
model based on gas pressure results in galactic HI mass fractions, M_HI/M_star,
that agree with observations from the GASS survey to better than 0.3 dex, but
the alternative theoretical H2 formula leads to a negative offset in
M_HI/M_star of up to 0.5 dex. Visual inspection reveals that most HI disks in
simulated HI-rich galaxies are vertically disturbed, plausibly due to recent
accretion events. Many galaxies (up to 80 per cent) contain spuriously large HI
holes, which are likely formed as a consequence of the feedback implementation
in EAGLE. The HI mass-size relation of all simulated galaxies is close to (but
16 per cent steeper than) observed, and when only galaxies without large holes
in the HI disc are considered, the agreement becomes excellent (better than 0.1
dex). The presence of large HI holes also makes the radial HI surface density
profiles somewhat too low in the centre, at \Sigma_HI > 1 M_Sun pc^-2 (by a
factor of <~ 2 compared to data from the Bluedisk survey). In the outer region
(\Sigma_HI < 1 M_Sun pc^-2), the simulated profiles agree quantitatively with
observations. Scaled by HI size, the simulated profiles of HI-rich (M_HI >
10^9.8 M_Sun) and control galaxies (10^9.1 M_Sun > M_HI > 10^9.8 M_Sun) follow
each other closely, as observed. (Abridged)
