  The inflow of cosmological gas onto haloes, while challenging to directly
observe and quantify, plays a fundamental role in the baryon cycle of galaxies.
Using the EAGLE suite of hydrodynamical simulations, we present a thorough
exploration of the physical properties of gas accreting onto haloes -- namely,
its spatial characteristics, density, temperature, and metallicity. Classifying
accretion as ``hot'' or `` cold'' based on a temperature cut of $10^{5.5}{\rm
K}$, we find that the covering fraction ($f_{\rm cov}$) of cold-mode accreting
gas is significantly lower than the hot-mode, with $z=0$ $f_{\rm cov}$ values
of $\approx 50\%$ and $\approx 80\%$ respectively. Active Galactic Nuclei (AGN)
feedback in EAGLE reduces inflow $f_{\rm cov}$ values by $\approx 10\%$, with
outflows decreasing the solid angle available for accretion flows. Classifying
inflow by particle history, we find that gas on first-infall onto a halo is
metal-depleted by $\approx 2$~dex compared to pre-processed gas, which we find
to mimic the circum-galactic medium (CGM) in terms of metal content. We also
show that high (low) halo-scale gas accretion rates are associated with
metal-poor (rich) CGM in haloes below $10^{12}M_{\odot}$, and that variation in
halo-scale gas accretion rates may offer a physical explanation for the
enhanced scatter in the star-forming main sequence at low
($\lesssim10^{9}M_{\odot}$) and high ($\gtrsim10^{10}M_{\odot}$) stellar
masses. Our results highlight how gas inflow influences several halo- and
galaxy-scale properties, and the need to combine kinematic and chemical data in
order to confidently break the degeneracy between accreting and outgoing gas in
CGM observations.
