Disk lifetime over CJ growth time with varying host mass M_⋆ and Ṁ_EPE. The color represents the values of τ_disk/τ_CJ. The contour line shows where the disk lifetime equals the CJ growth time. CJ-hosting systems are expected to lie below this line, while non-CJ systems lie above it. Our simulation results (Sect. 4) are over-plotted, with non-CJ systems shown as blue dots and CJ-hosting systems as red dots.