Left: comparison between the redshift evolution of the specific mass accretion rate (as derived from R_MM) and the specific star formation rate. The solid lines with the shaded regions are the best-fitting functions (and corresponding uncertainties) to the same R_MM data of the left panel of Fig. 5 at different merger timescales divided by the average mass ratio through cosmic time. The dot-dashed lines are several specific star formation rates from the literature (Dekel et al. 2009; Speagle et al. 2014; Tasca et al. 2015). The sSFR by Dekel et al. (2009) is normalized to sSFR(z = 0) = 0.1, as in Tasca et al. (2015). The dark cyan diamonds are the values by Khusanova et al. (2021) from the ALPINE survey. Right: Stellar mass accretion rate density (ρ_MM) as a function of redshift (top panel). Solid and dashed lines represent the best-fits to the data assuming double power-law, and combined power-law and exponential functions, respectively. The shaded regions highlight the uncertainties resulting from the choice of the fitting form. The colors correspond to alternative merger timescales and are the same as in the left panel. The dotted curve reports the mass accretion rate density, ρ_ill, obtained from the Illustris simulation, as described in the text. The dot-dashed red line shows the SFRD (ρ_SFRD) by Madau & Dickinson (2014). The red diamonds are the total SFRD values obtained from the ALPINE survey (Khusanova et al. 2021). Bottom panel: ratio between ρ_MM and ρ_SFRD as a function of cosmic time. The dashed horizontal line marks a ratio equal to 1.