Zoom-in intrinsic surface brightness maps (Fig. 1b) of the HzRGs sample to 15 × 15 arcsec² (or ∼110 × 110 pkpc²) around the central AGN (blue cross). In each panel, the blue+red and green solid lines indicate the direction of, and perpendicular to, the radio jet. The blue (red) colour represents the direction of the approaching (receding) jet. The white dashed line shows the flux-weighted position angle of the nebula (θ_weight). The white dotted line shows the unweighted position angle of the nebula (θ_unweight). The white star indicates the intrinsic flux-weighted centroid of the Lyα nebula. The flux weighted measurement is sensitive to the morphology of the high surface brightness part of the nebula. The unweighted measurement quantifies the morphology of the whole nebula. We find that nebula is elongated along the jet axis for most of HzRGs.