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It produces strong ultraviolet and optical emission that irradiates the planet-forming environment. In this work, we characterize the magnetospheric geometries, accretion rates, extinction properties, and hotspot structures of 67 T Tauri stars in the largest and most consistent study of ultraviolet and optical accretion signatures to date. To do so, we apply an accretion flow model to velocity-resolved H<jats:italic>\u03b1<\/jats:italic> profiles for T Tauri stars from the Hubble Space Telescope (HST) ULLYSES program with consistently derived stellar parameters. We find typical magnetospheric truncation radii to be almost half of the usually assumed value of 5 stellar radii. We then model the same stars\u2019 HST\/STIS spectra with an accretion shock model, finding a diverse range of hotspot structures. 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