We use numerical simulations in a Lambda CDM cosmology to model density profiles in a set of 16 dark matter haloes with resolutions of up to 7 million particles within the virial radius. These simulations allow us to follow robustly the formation and evolution of the central cusp over a large mass range of 10^11 to 10^14 M_sun, down to approximately 0.5% of the virial radius, and from redshift 5 to the present. The cusp of the density profile is set at redshifts of 2 or greater and remains remarkably stable to the present time, when considered in non-comoving coordinates. We fit our haloes to a 2 parameter profile where the steepness of the asymptotic cusp is given by gamma, and its radial extent is described by the concentration, c_gamma. In our simulations, we find gamma = 1.4 - 0.08Log(M/M_*) for haloes of 0.01M_* to 1000M_*, with a large scatter of gamma ~ +/-0.3$; and c_gamma = 8*M/M_*^{-0.15}, with a large M/M_* dependent scatter roughly equal to +/- c_gamma. Our redshift zero haloes have inner slope parameters ranging approximately from r^{-1} to r^{-1.5}, with a median of roughly r^{-1.3}. This 2 parameter profile fit works well for all our halo types, whether or not they show evidence of a steep asymptotic cusp. We also model a cluster in power law cosmologies of P ~ k^n (n=0,-1,-2,-2.7). We find larger concentration radii and shallower cusps for steeper n. The minimum resolved radius is well described by the mean interparticle separation. The trend of steeper and more concentrated cusps for smaller $M/M_*$ haloes clearly shows that dwarf sized Lambda CDM haloes have, on average, significantly steeper density profiles within the inner few percent of the virial radius than inferred from recent observations. Code to reproduce this profile can be downloaded from http://www.icc.dur.ac.uk/~reed/profile.html
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