Radial profiles of the surface brightness Fourier decomposition (asymmetry measurement). The c₀, c₁ and c₂ are the 0th, 1st and 2nd modes Fourier decomposition coefficients of the surface brightness radial profile, respectively (see den Brok et al. 2020, for definition). The (c₁/c₀)² + (c₂/c₀)² is a measurement of nebula asymmetry along the radial distance from the AGN. Our HzRGs are shown in solid colour lines. r_AGN is the radial distance measured from the central AGN. For comparison, we include the same measurements for the 4 nebulae of type-2 quasars from den Brok et al. (2020; grey dashed lines) and the type-2 from Sanderson et al. (2021; grey dot-dashed line). We also include the type-1 measurements from Borisova et al. (2016; dotted line represents the median and shaded region marks the 25th and 75th percentile, quantified by den Brok et al. 2020). The vertical shaded region is the 0.75 arcsec (∼25 ckpc) range affected by median seeing of our sample (the radial distance where the type-1 PSF is affected is ∼50 ckpc, see den Brok et al. 2020). The morphologies for most of the HzRGs nebulae are round (symmetric) ≲100 ckpc and become asymmetric at larger radial distances ∼100 ckpc (see text).