We report the discovery by the HATSouth exoplanet survey of three hot-Saturn transiting exoplanets: HATS-19b, HATS-20b, and HATS-21b. The planet host HATS-19 is a slightly evolved V = 13.0 G0 star with [Fe/H] = 0.240, a mass of 1.303 Msun, and a radius of 1.75 Rsun. HATS-19b is in an eccentric orbit (e = 0.30) around this star with an orbital period of 4.5697 days and has a mass of 0.427 Mjup and a highly inflated radius of 1.66 Rjup. The planet HATS-20b has a Saturn-like mass and radius of 0.273 Mjup and 0.776 Rjup respectively. It orbits the V = 13.8 G9V star HATS-20 (Ms = 0.910 Msun; Rs = 0.892 Rsun) with a period of 3.7993 days. Finally, HATS-21 is a V = 12.2 G4V star with [Fe/H] = 0.300, a mass of 1.080 Msun, and a radius of 1.021 Rsun. Its accompanying planet HATS-21b has a 3.5544-day orbital period, a mass of 0.332 Mjup, and a moderately inflated radius of 1.123 Rjup. With the addition of these three very different planets to the growing sample of hot-Saturns, we re-examine the relations between the observed giant planet radii, stellar irradiation, and host metallicity. We find a significant positive correlation between planet equilibrium temperature and radius, and a weak negative correlation between host metallicity and radius. To assess the relative influence of various physical parameters on observed planet radii, we train and fit models using Random Forest regression. We find that for hot-Saturns (0.1 < Mp < 0.5 Mjup), the planetary mass and equilibrium temperature play dominant roles in determining radii. For hot-Jupiters (0.5 < Mp < 2.0 Mjup), the most important parameter is equilibrium temperature alone. Finally, for irradiated higher-mass planets (Mp > 2.0 Mjup), we find that equilibrium temperature dominates in influence, with smaller contributions from planet mass and host metallicity.
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