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High-redshift radio galaxies (HzRGs, type-2 radio-loud quasars) host large-scale nebulae observed in the ionised gas differ from those seen in other types of high-redshift quasars. In this work, we exploit MUSE observations of Ly<jats:italic>\u03b1<\/jats:italic> nebulae around eight HzRGs (2.92\u2004&lt;\u2004<jats:italic>z<\/jats:italic>\u2004&lt;\u20044.51). All of the HzRGs have large-scale Ly<jats:italic>\u03b1<\/jats:italic> emission nebulae with seven of them extended over 100 pkpc at the observed surface brightness limit (\u223c2\u2005\u2212\u200520\u2005\u00d7\u200510<jats:sup>\u221219<\/jats:sup>\u2006erg\u2006s<jats:sup>\u22121<\/jats:sup>\u2006cm<jats:sup>\u22122<\/jats:sup>\u2006arcsec<jats:sup>\u22122<\/jats:sup>). Because the emission line profiles are significantly affected by neutral hydrogen absorbers across the entire nebulae extent, we performed an absorption correction to infer maps of the intrinsic Ly<jats:italic>\u03b1<\/jats:italic> surface brightness, central velocity, and velocity width, all at the last scattering surface of the observed Ly<jats:italic>\u03b1<\/jats:italic> photons. We find the following: (i) that the intrinsic surface brightness radial profiles of our sample can be described by an inner exponential profile and a power law in the low luminosity extended part; (ii) our HzRGs have a higher surface brightness and more asymmetric nebulae than both radio-loud and radio-quiet type-1 quasars; (iii) intrinsic nebula kinematics of four HzRGs show evidence of jet-driven outflows but we find no general trends for the whole sample; (iv) a relation between the maximum spatial extent of the Ly<jats:italic>\u03b1<\/jats:italic> nebula and the projected distance between the active galactic nuclei (AGN) and the centroids of the Ly<jats:italic>\u03b1<\/jats:italic> nebula; and (v) an alignment between radio jet position angles and the Ly<jats:italic>\u03b1<\/jats:italic> nebula morphology. All of these findings support a scenario in which the orientation of the AGN has an impact on the observed nebular morphologies and resonant scattering may affect the shape of the surface brightness profiles, nebular kinematics, and relations between the observed Ly<jats:italic>\u03b1<\/jats:italic> morphologies. Furthermore, we find evidence showing that the outskirts of the ionised gas nebulae may be \u2018contaminated\u2019 by Ly<jats:italic>\u03b1<\/jats:italic> photons from nearby emission halos and that the radio jet affects the morphology and kinematics of the nebulae. Overall, this work provides results that allow us to compare Ly<jats:italic>\u03b1<\/jats:italic> nebulae around various classes of quasars at and beyond cosmic noon (<jats:italic>z<\/jats:italic>\u2004\u223c\u20043).<\/jats:p>","DOI":"10.1051\/0004-6361\/202346415","type":"journal-article","created":{"date-parts":[[2023,10,14]],"date-time":"2023-10-14T18:57:08Z","timestamp":1697309828000},"page":"A70","source":"Crossref","is-referenced-by-count":14,"title":["3D tomography of the giant Ly<i>\u03b1<\/i> nebulae of <i>z<\/i> \u2248 3\u20135 radio-loud AGN"],"prefix":"10.1051","volume":"680","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7964-6749","authenticated-orcid":false,"given":"Wuji","family":"Wang","sequence":"first","affiliation":[]},{"given":"Dominika","family":"Wylezalek","sequence":"additional","affiliation":[]},{"given":"Jo\u00ebl","family":"Vernet","sequence":"additional","affiliation":[]},{"given":"Carlos","family":"De 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