The evolution of the Md-M_ and M-M_ correlations traces protoplanetary disc dispersal

(Abridged) Observational surveys of entire star-forming regions have provided evidence of power-law correlations between the disc properties and the stellar mass, especially the disc mass (Md ∝ M_*λₘ) and the accretion rate (M ∝ M_*^λacc). Whether the secular disc evolution affects said correlations is still debated: while the purely viscous scenario has been probed, other mechanisms could impact differently. We study the evolution of the slopes λₘ and λacc in the wind-driven and hybrid case and compare it to the viscous prediction, using a combination of analytical calculations and numerical simulations (performed with the 1D population synthesis code Diskpop, that we also present and release). Assuming Md(0) ∝ M_*^λm, 0 and M(0) ∝ M_*^λacc, 0 as initial conditions, we find that viscous and hybrid accretion preserve the shape of the correlations and evolve their slope; on the other hand, MHD winds change the shape of the correlations, bending them according to the scaling of the accretion timescale with the stellar mass. We also show how a spread in the initial conditions conceals this behaviour. We then analyse the impact of disc dispersal, and find that the currently available sample sizes (~ 30 discs at 5 Myr) introduce stochastic oscillations in the slopes evolution, which dominate over the physical signatures. Increasing the sample size could mitigate this issue: ~ 140 discs at 5 Myr, corresponding to the complete Upper Sco sample, would give small enough error bars to use the evolution of the slopes as a proxy for the driving mechanism of disc evolution. Finally, we discuss how the observational claim of steepening slopes necessarily leads to an initially steeper Md - M_* correlation with respect to M - M_*.