use a large number of particles per halo. We find that using $30$ particles provides reasonable results, but this imposes a rather high lower limit to halo masses of $2.2\times
10^{12}\,h^{-1}\,M_{\odot}$ for the large simulation, and $3.6\times 10^{9}\,h^{-1}\,M_{\odot}$ for the smaller one. We analised the distribution of angular momentum parameters and find that the reported high $\lambda$ tail (Bett et al., 2007) due to low number of particles per halo, is not present in any of our samples of DM haloes. We notice that the clustering signal in the small simulation on large scales may be affected by the small box size.

From this point on, we will centre most of our analysis on samples of DM haloes with different masses. From the small simulation we draw four DM halo subsamples separating haloes of different mass starting at a minimum of $100$ particles or $M\geq 1.2 \times 10^{10}\,h^{-1}\,M_{\odot}$ (the lowest mass sample considered includes haloes of up to 300 particles each; we do not use haloes of lower masses even though we are still above the minimum number of particles we consider safe to consider). Nine samples are drawn from the large simulation and contain DM haloes with more than 