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Abstract We present cosmological-scale three-dimensional neutral hydrogen (Hi) tomographic maps atz= 2–3 over a total of 837 deg²in two blank fields that are developed with Lyαforest absorptions of 14,736 background Sloan Digital Sky Survey (SDSS) quasars atz= 2.08–3.67. Using the tomographic maps, we investigate the large-scale (≳10h⁻¹cMpc) average Hiradial profiles and two-direction profiles of the line-of-sight (LOS) and transverse directions around galaxies and active galactic nuclei (AGNs) atz= 2–3 identified by the Hobby–Eberly Telescope Dark Energy eXperiment survey and SDSS, respectively. The peak of the Hiradial profile around galaxies is lower than the one around AGNs, suggesting that the dark matter halos of galaxies are less massive on average than those of AGNs. The LOS profile of AGNs is narrower than the transverse profile, indicating the Kaiser effect. There exist weak absorption outskirts at ≳30h⁻¹cMpc beyond Histructures of galaxies and AGNs found in the LOS profiles that can be explained by the Higas at ≳30h⁻¹cMpc falling toward the source position. Our findings indicate that the Hiradial profile of AGNs has transitions from proximity zones (≲a fewh⁻¹cMpc) to the Histructures (∼1–30h⁻¹cMpc) and the weak absorption outskirts (≳30h⁻¹cMpc). Although there is no significant dependence of AGN types (type 1 vs. type 2) on the Hiprofiles, the peaks of the radial profiles anticorrelate with AGN luminosities, suggesting that AGNs’ ionization effects are stronger than the gas mass differences.