consider halos with at least $30$ and $100$ particles in the large and small simulations, respectively, in order to ensure an accurate measurement of the halo angular momentum.

(430,250) (-40,0) (210,0)

The spatial halo-particle cross-correlation function $\xi(r)$ which we will use in this section, measures the excess probability with respect to a random distribution, that a DM particle will reside at a distance $r$ away from a given halo centre, in the volume element $dV$, $$dP=\bar{\nu}\left[ 1+\xi(r)\right] dV.  \label{definicion}$$ A standard method to measure $\xi(r)$ in a simulation box is to count pairs at a given distance bin, and then normalise this number by the expected number of pairs for a constant number density of objects. In our measurements we perform these counts stacking pairs depending on the angle between their position relative to the centre halo and its angular momentum. We consider tree cases, (i) using all pairs regardless of this angle (spherical shell volumes, isotropic case), (ii) using all pairs subtending an angle from the angular momentum less than a given threshold $\theta_1$ (parallel case), and (iii) adding pairs at lower inclinations than a limit angle $\theta_2$ from the perpendicular plane to the angular momentum (perpendicular case). We 