We present, for the first time, a clear N-body (NB) realization of the strong mass segregation solution for the stellar distribution around a massive black hole (MBH). We compare our NB results with those obtained by solving the orbit-averaged Fokker-Planck (FP) equation in energy space. The NB segregation is slightly stronger than in the FP solution, but both confirm the robustness of the regime of strong segregation when the number fraction of heavy stars is a (realistically) small fraction of the total population. In view of recent observations revealing a dearth of giant stars in the sub-parsec region of the Milky Way, we show that the timescales associated with cusp re-growth are not longer than (0.1 – 0.25) × T_rlx (r_h ). These timescales are shorter than a Hubble time for black holes masses M _• 4 × 10⁶ M _☉ and we conclude that quasi-steady, mass-segregated, stellar cusps may be common around MBHs in this mass range. Since extreme mass ratio inspirals detection rates by Laser Interferometer Space Antenna are expected to peak for M _• ~ 4 × 10⁵-10⁶ M _☉, a good fraction of these events should originate from strongly segregated stellar cusps.