and [haloes]{}. In [Section \[sec:data\]]{}, we present these simulations and the corresponding (sub-)halo catalogues. The different theoretical models of dimensionless spin parameters are described in [Section \[sec:theory\]]{}, while our results are summarized in [Section \[sec:results\]]{}. We discuss our work and conclude in [Section \[sec:discussion\]]{}.

Simulation Data {#sec:data}
===============

As we require our halo and subhalo masses to span a wide dynamic range ($10^{8}\lesssim\,M\,\lesssim10^{15}{\rm M_\odot}$) , we have run four dark matter only comoving cosmological boxes containing $512^3$ particles, with linear sizes of $8\,h^{-1}{\rm Mpc}$, $20\,h^{-1}{\rm
Mpc}$, $50\,h^{-1}{\rm Mpc}$, $100\,h^{-1}{\rm Mpc}$ respectively (hereafter BoxA, BoxB, BoxC, BoxD). The softening lengths are chosen to be $4\%$ of the mean separation between particles. This set of simulations can both sufficiently resolve subhalo spins [at least 300 particles per subhalo; @bett_2007] and have significant statistics for [haloes]{} (c.f. [Table \[tab:haloes\]]{}). We also ran two simulations with the same parameters as those used for the BoxA simulation except for the gravitational softening parameter. BoxA\_S1 has a smaller softening length whereas BoxA\_S2 has a larger softening length. We also ran a low resolution simulation containing $256^3$ particles and the same linear size, $8\,h^{-1}{\rm Mpc}$ as BoxA which we designate BoxLo. The mass resolution of BoxA ($2.6\times
