Context : The distribution of stars around a massive black hole ( MBH ) has been addressed in stellar dynamics for the last four decades by a number of authors . Because of its proximity , the centre of the Milky Way is the only observational test case where the stellar distribution can be accurately tested . Past observational work indicated that the brightest giants in the Galactic Centre ( GC ) may show a density deficit around the central black hole , not a cusp-like distribution , while we theoretically expect the presence of a stellar cusp . Aims : We here present a solution to this long-standing problem . Methods : We performed direct-summation N - body simulations of star clusters around massive black holes and compared the results of our simulations with new observational data of the GC ’ s nuclear cluster . Results : We find that after a Hubble time , the distribution of bright stars as well as the diffuse light follow power-law distributions in projection with slopes of \Gamma \approx 0.3 in our simulations . This is in excellent agreement with what is seen in star counts and in the distribution of the diffuse stellar light extracted from adaptive-optics ( AO ) assisted near-infrared observations of the GC . Conclusions : Our simulations also confirm that there exists a missing giant star population within a projected radius of a few arcsec around Sgr A* . Such a depletion of giant stars in the innermost 0.1 pc could be explained by a previously present gaseous disc and collisions , which means that a stellar cusp would also be present at the innermost radii , but in the form of degenerate compact cores .