choose the threshold angles, for the parallel and perpendicular cases mentioned above ($\theta_1$ and $\theta_2$, respectively), so that the volumes in each case are the same. This can be achieved by setting, $\sin(\theta_2)=1-\cos(\theta_1)=\chi$, and choosing a value for the threshold parameter $\chi$. Selecting $\chi\leq0.5$ implies angles $\theta_1 \leq 60^o$ and $\theta_2 \leq 30^o$. Throughout this paper we use $\chi=0.5$.

Errors in the correlation function are estimated using the jacknife technique, with a total of $50$ subsamples for the numerical simulation ($20$ jacknifes for the SDSS data analysis). We find that our errors are stable for this number of jacknife subsamples (we tested from $20$ to $100$) and does not produce underestimations. In the case of quotients between correlation functions, we apply the jacknife technique to the actual measurement of the ratio. We adopt the jacknife technique since it has been reported to provide similar error estimates to those obtained from independent samples (see for instance, Padilla et al., 2004).

Simulation results {#simresult}
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The analysis of alignments of structure with the angular momentum of DM haloes presents a first difficulty in that in order to obtain a reliable and stable direction for the halo spin, it is often necessary to 