Histograms of binary pair-up radii R_pair (in units of Schwarzschild radii) for first-generation (1g) and Nth-generation (Ng) BHs, across a range of SMBH masses (log M_•/M_⊙ = 6, 7, 8 in the three columns, respectively) and viscosity parameters (upper row: α = 0.01; lower row: α = 0.1). Panels show the pair-up radii probability density functions (PDFs), normalized separately in each panel. The 1g distributions are shown as step histograms, while Ng distributions are overlaid either as filled or hatched histograms for visual distinction. Vertical dotted lines indicate the positions of migration traps identified from the torque profile. Color represents the migration model used (green: G24; purple: B16).