TRINITY III: Quasar Luminosity Functions Decomposed by Halo, Galaxy, and Black Hole Masses and Eddington Ratios from z=0-10

We present the redshift evolution of quasar luminosity functions decomposed by halo mass, galaxy mass, supermassive black hole (SMBH) mass, and Eddington ratio, as well as SMBH kinetic/radiative energy output ratios from TRINITY, a flexible empirical model that self-consistently infers the halo--galaxy--SMBH connection that match observational data. Key findings include: 1) The normalization of QLF increases by ~3-4 dex from z~10 to z~4, due to the fast mass build-up of different SMBH populations; 2) From z~4 to z~1, less massive galaxies and SMBHs make up bigger and bigger fractions of QLFs, due to the AGN downsizing effect; 3) At z~0, massive haloes/galaxies/SMBHs are responsible for most bright quasars due to low Eddington ratios among all SMBHs; 4) The bright ends of quasar luminosity functions (QLFs) are dominated by SMBHs that are at least 0.3 dex over-massive relative to the median SMBH mass-galaxy mass relation; 5) QLFs at z~6-7 are dominated by SMBHs accreting at Eddington ratios 0.1 < $\eta_\mathrm{rad}$ < 1, but super-Eddington AGNs contribute more significantly to QLFs towards z~9-10.