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We use the 30 simulations of the Auriga Project to estimate the temporaldependency of the inflow, outflow and net accretion rates onto the discs ofMilky Way-like galaxies. The net accretion rates are found to be similar forall galaxies at early times, increasing rapidly up to $\sim 10~\mathrm{M}_\odot\, \mathrm{yr}^{-1}$. After $\sim 6~\mathrm{Gyr}$ of evolution, however, thenet accretion rates are diverse: in most galaxies, these exhibit anexponential-like decay, but some systems instead present increasing orapproximately constant levels up to the present time. An exponential fit to thenet accretion rates averaged over the MW analogues yields typical decaytime-scale of $7.2~\mathrm{Gyr}$. The analysis of the time-evolution of theinflow and outflow rates, and their relation to the star formation rate (SFR)in the discs, confirms the close connection between these quantities. First,the inflow$/$outflow ratio stays approximately constant, with typical values of$\dot{M}_\mathrm{out}/ \dot{M}_\mathrm{in} \sim 0.75$, indicating that the gasmass involved in outflows is of the order of 25% lower compared to thatinvolved in inflows. A similar behaviour is found for the SFR$/$inflow rateratio, with typical values between 0.1 and 0.3, and for the outflow rate$/$SFRwhich varies in the range $3.5$--$5.5$. Our results show that continuous inflowis key to the SFR levels in disc galaxies, and that the star formation activityand the subsequent feedback in the discs is able to produce mass-loaded galaxywinds in the disc-halo interface.

Cosmological gas accretion history onto the stellar discs of Milky Way-like galaxies in the Auriga simulations -- (I) Temporal dependency