  We present cosmological-scale 3-dimensional (3D) neutral hydrogen ({\sc Hi})
tomographic maps at $z=2-3$ over a total of 837 deg$^2$ in two blank fields
that are developed with Ly$\alpha$ forest absorptions of 14,736 background
Sloan Digital Sky Survey (SDSS) quasars at $z$=2.08-3.67. Using the tomographic
maps, we investigate the large-scale ($\gtrsim 10$ $h^{-1}$cMpc) average {\sc
Hi} radial profiles and two-direction profiles of the line-of-sight (LoS) and
transverse (Trans) directions around galaxies and AGN at $z=2-3$ identified by
the Hobby-Eberly Telescope Dark Energy eXperiment (HETDEX) and SDSS surveys,
respectively. The peak of the {\sc Hi} radial profile around galaxies is lower
than the one around AGN, suggesting that the dark-matter halos of galaxies are
less massive on average than those of AGN. The LoS profile of AGN is narrower
than the Trans profile, indicating the Kaiser effect. There exist weak
absorption outskirts at $\gtrsim 30$ $h^{-1}$cMpc beyond {\sc Hi} structures of
galaxies and AGN found in the LoS profiles that can be explained by the {\sc
Hi} gas at $\gtrsim 30$ $h^{-1}$cMpc falls toward the source positions. Our
findings indicate that the {\sc Hi} radial profile of AGN has transitions from
proximity zones ($\lesssim$ a few $h^{-1}$cMpc) to the {\sc Hi} structures
($\sim 1-30$ $h^{-1}$cMpc) and the weak absorption outskirts ($\gtrsim 30$
$h^{-1}$cMpc). Although there is no significant dependence of AGN types (type-1
vs. type-2) on the {\sc Hi} profiles, the peaks of the radial profiles
anti-correlate with AGN luminosities, suggesting that AGN's ionization effects
are stronger than the gas mass differences.
