  We examine the properties of atomic hydrogen (HI) associated with galaxies in
the EAGLE simulations of galaxy formation. EAGLE's feedback parameters were
calibrated to reproduce the stellar mass function and galaxy sizes at $z=0.1$,
and we assess whether this calibration also yields realistic HI properties. We
estimate the self-shielding density with a fitting function calibrated using
radiation transport simulations, and correct for molecular hydrogen with
empirical or theoretical relations. The `standard-resolution' simulations
systematically underestimate HI column densities, leading to an HI deficiency
in low-mass ($M_\star < 10^{10}M_\odot$) galaxies and poor reproduction of the
observed HI mass function. These shortcomings are largely absent from EAGLE
simulations featuring a factor of 8 (2) better mass (spatial) resolution,
within which the HI mass of galaxies evolves more mildly from $z=1$ to $0$ than
in the standard-resolution simulations. The largest-volume simulation
reproduces the observed clustering of HI systems, and its dependence on
HI-richness. At fixed $M_\star$, galaxies acquire more HI in simulations with
stronger feedback, as they become associated with more massive haloes and
higher infall rates. They acquire less HI in simulations with a greater star
formation efficiency, since the star formation and feedback necessary to
balance the infall rate is produced by smaller gas reservoirs. The simulations
indicate that the HI of present-day galaxies was acquired primarily by the
smooth accretion of ionized, intergalactic gas at $z\simeq1$, which later
self-shields, and that only a small fraction is contributed by the
reincorporation of gas previously heated strongly by feedback. HI reservoirs
are highly dynamic: over $40$ percent of HI associated with $z=0.1$ galaxies is
converted to stars or ejected by $z=0$.
