(a) Intrinsic flux-weighted ellipticity (sensitive to the morphology of the high surface brightness part of the nebula), e_weight, versus distance offset between nebular centroid and AGN position, d_{AGN − neb}. The typical uncertainty of d_{AGN − neb} (σ_{dAGN − neb} = 0.4 pkpc, Table 3) is shown at bottom left. (b) Maximum Lyα nebula linear extent, d_max, versus d_{AGN − neb}. In both panels, we give the Spearman correlation measurements for our sample at the top left (the star superscript indicates the correlation is calculated excluding MRC 0316-257 in panel a). We also include the data from Arrigoni Battaia et al. (2019) in both panels in grey (radio quiet) and pink (radio loud) dots. We note that the Arrigoni Battaia et al. (2019) sample shown in this figure is incomplete to concentrate on the relation for our targets. There are positive correlations detected for e_weight–d_{AGN − neb} and d_max–d_{AGN − neb}.