redshift dependence of the halo vs. subhalo spin distribution offset. In [Figure \[piclm1\]]{} and [Figure \[piclm2\]]{},we give the Peebles and Bullock spin distributions of (sub-)[haloes]{} at $z=0$, $z=0.84$, $z=2.38$ and $z=5.21$, respectively. The spin of sub[haloes]{} at the lower mass end decreases significantly with time, while the spin of massive [haloes]{}increases slightly with time. We calculate the $\lambda_0$($\lambda_0'$) in each mass bin and then use a linear function $log\lambda_0=a*log(M/10^{10}h^{-1}M_{\odot})+b$ ($\lambda_0'$ for Bullock spin) to fit $\lambda_0$($\lambda_0'$) against mass. We list the parameters of each fitting line in [Table \[tab:ab\]]{}. It is clear the difference between the halo and subhalo spin distribution increases with time. This is consistent with the argument that tidal stripping causes the difference. Affected by stripping, sub[haloes]{} loose more and more high angular momentum particles as time passes.

To confirm this result we checked how the spin of a single halo changes with time. We randomly select 6 sub[haloes]{} and plot their spin against redshift. We constrain the samples selected so that they are likely to be the sub[haloes]{} heavily stripped. As expected, heavily stripped sub[haloes]{} should have low mass (here we choose masses less than $10^{9}h^{-1}M_{\odot}$) and have long histories, forming prior to redshift 8. As 