  We use the EAGLE suite of hydrodynamical simulations to analyse accretion
rates (and the breakdown of their constituent channels) onto haloes over cosmic
time, comparing the behaviour of baryons and dark matter (DM). We also
investigate the influence of sub-grid baryon physics on halo-scale inflow,
specifically the consequences of modelling radiative cooling, as well as
feedback from stars and active galactic nuclei (AGN). We find that variations
in halo baryon fractions at fixed mass (particularly their circum-galactic
medium gas content) are very well correlated with variations in the baryon
fraction of accreting matter, which we show to be heavily suppressed by stellar
feedback in low-mass haloes, $M_{\rm halo}\lesssim10^{11.5}M_{\odot}$. Breaking
down accretion rates into first infall, recycled, transfer and merger
components, we show that baryons are much more likely to be smoothly accreted
than to have originated from mergers when compared to DM, finding (averaged
across halo mass) a merger contribution of $\approx6\%$ for baryons, and
$\approx15\%$ for DM at $z\approx0$. We also show that the breakdown of inflow
into different channels is strongly dependent on sub-grid physics, particularly
the contribution of recycled accretion (accreting matter that has been
previously ejected from progenitor haloes). Our findings highlight the dual
role that baryonic feedback plays in regulating the evolution of galaxies and
haloes: by (i) directly removing gas from haloes, and (ii) suppressing gas
inflow to haloes.
