Two-body energy exchange between stars orbiting massive black holes ( MBHs ) leads to the formation of a power-law density distribution n ( r ) \propto r ^ { - \alpha } that diverges towards the MBH .
For a single mass population , \alpha = 7 / 4 and the flow of stars is much less than N ( < r ) / t _ { r } ( enclosed number of stars per relaxation time ) .
This “ zero-flow ” solution is maintained for a multi-mass system for moderate mass ratios or systems where there are many heavy stars , and slopes of 3 / 2 < \alpha < 2 are reached , with steeper slopes for the more massive stars .
If the heavy stars are rare and massive however , the zero-flow limit breaks down and much steeper distributions are obtained .

We discuss the physics driving mass-segregation with the use of Fokker-Planck calculations , and show that steady state is reached in 0.2 - 0.3 ~ { } t _ { r } .
Since the relaxation time in the Galactic centre ( GC ) is t _ { r } \sim 2 - 3 \times 10 ^ { 10 } { yr } , a cusp should form in less than a Hubble time .
The absence of a visible cusp of old stars in the GC poses a challenge to these models , suggesting that processes other than two-body relaxation have played a role .
We discuss astrophysical processes within the GC that depend crucially on the details of the stellar cusp .