We use numerical simulations in a \Lambda CDM cosmology to model density profiles in a set of sixteen dark matter haloes with resolutions of up to seven 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 } _ { \odot } , down to approximately 0.5 \% of the virial radius , and from redshift 5 to the present , covering a larger range in parameter space than previous works .
We confirm that the cusp of the density profile is set at redshifts of two or greater and remains remarkably stable to the present time , when considered in non-comoving coordinates .

Motivated by the diversity and evolution of halo profile shapes , we fit our haloes to the two parameter profile , \rho \propto { 1 \over ( c _ { \gamma } r / r _ { vir } ) ^ { \gamma } [ 1 + ( c _ { \gamma } r / r _ { vir% } ) ] ^ { 3 - \gamma } } , where the steepness of the cusp is given by the asymptotic inner slope parameter , \gamma , and its radial extent is described by the concentration parameter , c _ { \gamma } ( with c _ { \gamma } 
defined as the virial radius divided by the concentration radius ) .
In our simulations , we find \gamma \simeq 1.4 - 0.08 Log _ { 10 } ( M / M _ { * } ) for haloes of 0.01 M _ { * } to 1000 M _ { * } , with a large scatter of \Delta \gamma \sim \pm 0.3 , where M _ { * } is the redshift dependent characteristic mass of collapsing haloes ; and c _ { \gamma } \simeq 8. ( M / M _ { * } ) ^ { -0.15 } , with a large M / M _ { * } dependent scatter roughly equal to \pm c _ { \gamma } .
Our redshift zero haloes have inner slope parameters ranging approximately from r ^ { -1 } ( i.e .
Navarro , Frenk , & White ) to r ^ { -1.5 } ( i.e .
Moore et al .
) , with a median of roughly r ^ { -1.3 } .
This two parameter profile fit works well for all types haloes in our simulations , whether or not they show evidence of a steep asymptotic cusp .
We also model a cluster in power law cosmologies of P \propto k ^ { n } , with n = ( 0 , -1 , -2 , -2.7 ) .
Here we find that the concentration radius and the inner cusp slope are a both function of n , with larger concentration radii and shallower cusps for steeper power spectra .

We have completed a thorough resolution study and find that the minimum resolved radius is well described by the mean interparticle separation over a range of masses and redshifts .
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/ \sim reed/profile.html .