We analyze deep near-IR adaptive optics imaging ( taken with NAOS/CONICA on the VLT ) Based on observations obtained at the European Southern Observatory , Chile as well as new proper motion data of the nuclear star cluster of the Milky Way . The surface density distribution of faint ( H \leq 20 , K _ { s } \leq 19 ) stars peaks within 0.2 ^ { \prime \prime } of the black hole candidate SgrA ^ { \star } . The radial density distribution of this stellar ’ cusp ’ follows a power law of exponent \alpha \sim 1.3 - 1.4 . The K-band luminosity function of the overall nuclear stellar cluster ( within 9 ^ { \prime \prime } of SgrA ^ { \star } ) resembles that of the large scale , Galactic bulge , but shows an excess of stars at K _ { s } \leq 14 . It fits population synthesis models of an old , metal rich stellar population with a contribution from young , early and late-type stars at the bright end . In contrast , the cusp within \leq 1.5 ^ { \prime \prime } of SgrA ^ { \star } appears to have a featureless luminosity function , suggesting that old , low mass horizontal branch/red clump stars are lacking . Likewise there appear to be fewer late type giants . The innermost cusp also contains a group of moderately bright , early type stars that are tightly bound to the black hole . We interpret these results as evidence that the stellar properties change significantly from the outer cluster ( \geq a few arcsecs ) to the dense innermost region around the black hole . We find that most of the massive early type stars at distances 1-10 ” from SgrA ^ { \star } are located in two rotating and geometrically thin disks . These disks are inclined at large angles and counter-rotate with respect to each other . Their stellar content is essentially the same , indicating that they formed at the same time . We conclude that of the possible formation scenarios for these massive stars the most probable one is that 5-8 million years ago two clouds fell into the center , collided , were shock compressed and then formed two rotating ( accretion ) disks orbiting the central black hole . For the OB-stars in the central arcsecond , on the other hand , a stellar merger model is the most appealing explanation . These stars may thus be ’ super-blue-stragglers ’ , formed and ‘ rejuvenated ’ through mergers of lower mass stars in the very dense ( \geq 10 ^ { 8 } M _ { \odot } pc ^ { -3 } ) environment of the cusp . The ‘ collider model ’ also accounts for the lack of giants within the central few arcseconds . The star closest to SgrA ^ { \star } in 2002 , S2 , exhibits a 3.8 \micron excess . We propose that the mid-IR emission either comes from the accretion flow around the black hole itself , or from dust in the accretion flow that is heated by the ultra-violet emission of S2 .