derived spin of (sub-)[haloes]{}. @maccio_2008 has tested halo spins with different cosmological parameters. They found that the spin distributions of [haloes]{} is essentially independent of cosmology, at least for changes between WMAP1,WMAP3 and WMAP5. We choose not to confirm this result here. BoxA, BoxA\_S1 and BoxA\_S2 are used to compare different force resolutions. BoxA and BoxLo are used to compare different mass resolutions. To ensure reliable properties are recovered only (sub-)[haloes]{} with more than 300 particles are selected throughout this work. While calculating the spin of [haloes]{}, all their substructures are removed from them. Spin distributions are fitted by [Equation \[eqn:bettfit\]]{} and [Equation \[eqn:bullockfit\]]{}, and the fitting parameters are listed in [Table \[tab:codes\]]{}.

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                     $\lambda_0$           $\alpha$            $\lambda_0$            $\alpha$
     BoxA\_S1    $0.0398\pm0.00019 $   $ 2.54\pm0.039 $    $ 0.0237\pm0.00032 $    $ 3.56\pm0.13$
     BoxA        $0.0371\pm0.00021 $   $ 2.59\pm0.047 $    $ 0.0254\pm0.00049 $    $ 2.92\pm0.17$
     BoxA\_S2    $0.0364\pm0.00026 $   $ 2.59\pm0.058 $    $ 0.0298\pm0.00036 $    $ 2.60\pm0.10$
     BoxA\_S1    $0.0390\pm0.00024 $   $ 2.42\pm0.049 $    $ 0.0260\pm0.00029 $    $ 2.89\pm0.10$
     BoxA        $0.0366\pm0.00019 $   $ 2.48\pm0.042 $    $ 0.0277\pm0.00027 $    $ 2.68\pm0.08$
     BoxA\_S2    $0.0356\pm0.00021 $   $ 2.37\pm0.046 $    $ 0.0322\pm0.00033 $    $ 2.52\pm0.08$
     BoxA\_S1    $0.0380\pm0.00024 $   $ 2.82\pm0.053 $    $ 0.0303\pm0.00044 $    $ 2.53\pm0.12$
     