missed by [<span style="font-variant:small-caps;">ahf</span>]{}. Difficulties for [<span style="font-variant:small-caps;">ahf</span>]{} in resolving substructures where the density contrast between the subhalo and the main halo is expected to be small have also been reported elsewhere [@Avila_2014]. Further evidence for this issue is the rising incidence of missing substructures as the box size is increased evidenced in [Table \[tab:haloes\]]{}: for the largest box (BoxD), [<span style="font-variant:small-caps;">ahf</span>]{}misses $71\%$ of the sub[haloes]{} found by [<span style="font-variant:small-caps;">subfind</span>]{}. [<span style="font-variant:small-caps;">ahf</span>]{} is missing small sub[haloes]{} in the outskirts of the host halo and (as we shall demonstrate later) these small sub[haloes]{} are precisely the ones with the lowest spin parameters.

This naturally produces a population of sub[haloes]{} with higher average spin parameter for [<span style="font-variant:small-caps;">ahf</span>]{}. As [<span style="font-variant:small-caps;">hbt</span>]{} and [<span style="font-variant:small-caps;">subfind</span>]{} produce consistent results and [<span style="font-variant:small-caps;">ahf</span>]{} fails to recover the complete subhalo population we choose to concentrate our analysis on [<span style="font-variant:small-caps;">subfind</span>]{} for the remainder of this paper.

\[tab:res\]

  ------------------------ ----------------------- ------------------- ---------------------- ------------------
                                                                                              
                                 $\lambda_0$            $\alpha$            $\lambda_0$            $\alpha$
  BoxA($N_p\ge300$)         $ 0.0371\pm0.00021 $    $ 2.59\pm0.047 $    $ 0.0254\pm0.00049 $    $ 2.92\pm0.17$
  BoxA($N_p\ge2400$)        $ 0.0393\pm0.00062  $   $ 2.53\pm0.13  $    $ 0.0281\pm0.0011  $    $ 2.78\pm0.33$
  BoxA\_S2($N_p\ge2400$)    $ 0.0389\pm0.00069  $   $ 2.48\pm0.14  $    $ 0.0288\pm0.0010  $    $ 2.51\pm0.29$
  BoxLo($N_p\ge300$)        $ 0.0392\pm0.00073  $   