Little Red Dot $-$ Host Galaxy $=$ Black Hole Star: A Gas-Enshrouded Heart at the Center of Every Little Red Dot

The central engines of Little Red Dots (LRDs) may be ``black hole stars" (BHs), early stages of black hole growth characterized by dense gas envelopes. So far, the most direct evidence for BHs comes from a handful of sources where the host galaxy is completely outshone as suggested by their remarkably steep Balmer breaks. Here we present a novel scheme to disentangle BHs from their host galaxies assuming that the [OIII]5008Å line arises exclusively from the host. Using a sample of 98 LRDs ($z$~$2-9$) with high quality NIRSpec/PRISM spectra, we demonstrate that the host-subtracted median stack displays a Balmer break $>2\times$ stronger than massive quiescent galaxies, with the rest-optical continuum resembling a blackbody-like SED ($T_{\mathrm{e}\mathrm{f}\mathrm{f}}$~$4050$ K, $\log (L_{\mathrm{b}\mathrm{o}\mathrm{l}})$~$43.9$ erg s${}^{-1}$, $R_{\mathrm{e}\mathrm{f}\mathrm{f}}$~$1300$ au). We measure a steep Balmer decrement (H$\alpha$/H$\beta >10$) and numerous density-sensitive features (e.g., FeII, HeI, OI). These are hallmark signatures of dense gas envelopes, providing population-level evidence that BHs indeed power LRDs. In the median LRD, BHs account for $\sim 20\mathrm{\%}$ of the UV emission, $\sim 50\mathrm{\%}$ at the Balmer break, and $\sim 90\mathrm{\%}$ at wavelengths longer than H$\alpha$ with the remainder arising from the host. BHs preferentially reside in low-mass galaxies ($M_{\star }$~${10}^8{\mathrm{M}}_{\odot }$) undergoing recent starbursts, as evidenced by extreme emission line EWs (e.g., [OIII]5008Å~$1100$Å, CIII]~$12$Å), thereby favoring BH* origins linked to star-formation. We show V-shaped LRD selections are biased to high BH*/host fractions ($\gtrsim 60\mathrm{\%}$ at 5500Å) – less dominant BHs may be powering JWST’s blue broad-line AGN. We find BHs are so commonplace and transient (duty cycle $\sim 1\mathrm{\%}$, lifetime $\sim 10$ Myrs) that every massive black hole may have once shone as a BH*.