Orbital dynamics in the (r, r _p ) phase space, where r is the semimajor axis and r _p is the periapsis. The dashed black line distinguishes between the two-body-scattering-dominated region and the GW-dominated one (Equation (7)); above it, the scattering leads to a diffusion dominantly in the r _p -direction (as encapsulated by the shaded vertical blue funnel), while below it, GW emission efficiently shrinks and circularizes the orbit (along the horizontal shaded funnel). The red dashed–dotted line marks the mostly bound orbit, with r _p = 4R _s , and the yellow dashed–dotted line represents the critical semimajor axis R _c , (Equation (8)), separating EMRI progenitors (with r ≲ R _c ) and plunge progenitors (with r ≳ R _c ). The gray lines demonstrate examples of trajectories leading to an EMRI or a plunge, according to their initial semimajor axis.