The centre of the Milky Way is the nearest nucleus of a galaxy and offers a unique possibility to study the structure and dynamics of a dense stellar cluster around a super-massive black hole. We present high-resolution seeing limited and AO NIR imaging observations of the stellar cluster within about one parsec of Sgr A*, the massive black hole at the centre of the Milky Way. Stellar number counts and the diffuse background light density were extracted from these observations in order to examine the structure of the nuclear stellar cluster. A detailed map of the variation of interstellar extinction in the central 0.5 pc of the Milky Way is presented and used to correct the stellar number counts and diffuse light density. Our findings are as follows: (a) A broken-power law provides an excellent fit to the overall structure of the GC nuclear cluster. The power-law slope of the cusp is \Gamma=0.19+/-0.05, the break radius is R_break = 6.0'' +/- 1.0'' or 0.22+/-0.04 pc, and the cluster density decreases with a power-law index of \Gamma=0.75+/-0.1 outside of R_ break. (b) Using the best velocity dispersion measurements from the literature, we derive higher mass estimates for the central parsec than assumed until now. The inferred density of the cluster at the break radius is 2.8+/-1.3* 106 M_o pc-3. This high density agrees well with the small extent and flat slope of the cusp. Possibly, the mass of the stars makes up only about 50% of the total cluster mass. (c) Possible indications of mass segregation in the cusp are found (d) The cluster appears not entirely homogeneous. Several density clumps are detected that are concentrated at projected distances of R=3'' and R=7'' from Sgr A*.(e) There appears to exist an under-density of horizontal branch/red clump stars near R=5'', or an over-density of stars of similar brightness at R=3'' and R=7''. (f) The extinction map in combination with cometary-like features in an L'-band image may provide support for the assumption of an outflow from Sgr A*.