Lyα Nebulae in HETDEX: The Largest Statistical Census Bridging Lyα Halos and Blobs across Cosmic Noon

The Hobby-Eberly Dark Energy Experiment (HETDEX) is an untargeted ~540 deg^2 spectroscopic survey of Lyα emission in the 1.9 < z < 3.5 Universe. In surface brightness, this survey reaches 1σ Lyα sensitivities of approximately 2-5 x 10^-18 erg s^-1 cm^-2 arcsec^-2, allowing large samples of extended Lyα nebulae (LAN) to be studied. We selected a sample of 70,691 Lyα-emitting galaxies (LAEs) with an emission-line signal-to-noise ratio greater than 6 and modeled the Lyα emission as a point-source component with an optional exponential envelope. Half (~47.5%) of the LAE sample (33,612 objects) exhibits significant extended emission and is best fit by the two-component model. The fraction of resolved sources increases with Lyα flux and luminosity. Their isophotal areas range from 10-130 arcsec^2 (median 15 arcsec^2), with integrated Lyα fluxes from 6-2000 x 10^-17 erg s^-1 cm^-2 (median 20 x 10^-17 erg s^-1 cm^-2). Comparison between point-spread-function-weighted and isophotal flux measurements shows that the HETDEX pipeline underestimates the total Lyα flux by ~30% on average, reflecting the substantial halo contribution in extended sources. Approximately 420 LANs are found per deg^2 over 79.5 deg^2 of non-contiguous sky. About 12% of resolved sources show active galactic nuclei signatures and are bright in Lyα and continuum. The remaining 88% span a wide range of morphologies and often lack continuum counterparts. Exponential scale lengths show no strong correlation with Lyα flux or luminosity (median 11.6 +/- 1.9 kpc). Only 2.9% of the full S/N > 6 LAE population with ancillary data have radio counterparts, but 64% of those are found to be extended, with the radio fraction increasing with Lyα size.