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We present a catalogue of 362 million stellar parameters, distances, andextinctions derived from Gaia's early third data release (EDR3) cross-matchedwith the photometric catalogues of Pan-STARRS1, SkyMapper, 2MASS, and AllWISE.The higher precision of the Gaia EDR3 data, combined with the broad wavelengthcoverage of the additional photometric surveys and the new stellar-densitypriors of the {\tt StarHorse} code allow us to substantially improve theaccuracy and precision over previous photo-astrometric stellar-parameterestimates. At magnitude $G=14\, (17)$, our typical precisions amount to 3%(15%) in distance, 0.13 mag (0.15 mag) in $V$-band extinction, and 140 K (180K) in effective temperature. Our results are validated by comparisons with openclusters, as well as with asteroseismic and spectroscopic measurements,indicating systematic errors smaller than the nominal uncertainties for thevast majority of objects. We also provide distance- and extinction-correctedcolour-magnitude diagrams, extinction maps, and extensive stellar density mapsthat reveal detailed substructures in the Milky Way and beyond. The new densitymaps now probe a much greater volume, extending to regions beyond the Galacticbar and to Local Group galaxies, with a larger total number density. We publishour results through an ADQL query interface ({\tt gaia.aip.de}) as well as viatables containing approximations of the full posterior distributions. Ourmulti-wavelength approach and the deep magnitude limit make our results usefulalso beyond the next Gaia release, DR3.

Photo-astrometric distances, extinctions, and astrophysical parameters for Gaia EDR3 stars brighter than G=18.5