  One of the fundamental assumptions of chemical evolution models (CEMs) of the
Milky Way (MW) and other spirals is that higher gas accretion rates are
expected in the past, and in the inner regions of the Galaxy. This leads to the
so-called `inside-out disc formation scenario'. Yet, these are probably the
most unconstrained inputs of such models. In the present paper, we aim at
investigating these main assumptions by studying how gas is accreted in four
simulated MW-like galaxies assembled within the $\Lambda$CDM scenario. The
galaxies were obtained using two different simulation techniques, cosmological
setups and initial conditions. Two of them are MW candidates corresponding to
the chemodynamical model of Minchev et al. (2013, 2014) (known as MCM) and the
Local Group cosmological simulation of Nuza et al. (2014). We investigate
vertical and radial gas accretion on to galaxy discs as a function of cosmic
time and disc radius. We find that accretion in the MW-like galaxies seem to
happen in two distinct phases, namely: an early, more violent period; followed
by a subsequent, slowly declining phase. Our simulations seem to give support
to the assumption that the amount of gas incorporated into the MW disc
exponentially decreases with time, leading to current net accretion rates of
$0.6-1\,$M$_\odot\,$yr$^{-1}$. In particular, accretion timescales on to the
simulated thin-disc-like structures are within $\sim5-7\,$Gyr, consistent with
expectations from CEMs. Moreover, our simulated MW discs are assembled from the
inside-out with gas in the inner disc regions accreted in shorter timescales
than in external ones, in qualitative agreement with CEMs of the Galaxy.
However, this type of growth is not general to all galaxies and it is
intimately linked to their particular merger and gas accretion history.
