${\sigma }_{M_0}-{\sigma }_{t_{\text{acc},0}}$ plane with the values of R² for different values of age t. The colored dots in every plot are Monte Carlo simulations of 10⁵ proto-planetary disks with ω = 0.2, evolving following Eqs. (4), (5), where M₀ and t_acc,0 follow a lognormal distribution centered on the natural logarithm of 0.1 M_⊙ and 1 Myr, respectively. The hatched contours represent the regions where there is no correlation between M_D and Ṁ_*, while the dashed line represents the points where ${\sigma }_{M_0}-{\sigma }_{t_{\text{acc},0}}$.