$\varphi -{\sigma }_{M_0}$ plane with the values of the slope γ and the spread of the M_D−Ṁ_* correlation σ. Shown in orange are the values γ ∊ [0.5,0.9], while in light blue the values σ ∊ [0.55,0.71] dex as they confine the region of values compatible with the values found in Manara et al. (2016). The colored regions show the value of γ and σ for Monte Carlo disk populations obtained with the corresponding specific values of ϕ and ${\sigma }_{M_0}$. Every Monte Carlo consists of 10⁴ disks evolving according to Eqs. (4), (5), where $M_0\propto t_{\text{acc},0}^{\varphi }$, ω = 0.8, t = 2 Myr, and t_acc,0 follows a lognormal distribution centered on the values retrieved from the fit in Sect. 4.1. The cross shows the case investigated by Tabone et al. (2022b).