The mass of a BH at which the ADIOS state is realized due to accretion growth prior to kicks, as a function of distance from the SMBH in the TQM model, assuming an initial BH mass of m = 5 M_⊙. For the regions where m = 5 M_⊙, the ADIOS state is realized (r_circ > r_trap) without any growth. For m > 5 M_⊙, the initial state is ZEBRA. As the BH rapidly grows, the AGN surface density decreases due to gap formation, reducing r_trap. Eventually, the ADIOS state is realized (r_circ = r_trap) after growth to the value shown. The vertical green and red lines mark the locations where H_AGN/R_BH reaches a minimum and where the Toomre parameter becomes Q≥1, respectively.