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We present a sample of 34 normal SNe II detected with the Zwicky TransientFacility, with multi-band UV light-curves starting at $t \leq 4$ days afterexplosion, as well as X-ray detections and upper limits. We characterize theearly UV-optical colors and provide prescriptions for empirical host-extinctioncorrections. We show that the $t > 2\,$days UV-optical colors and the blackbodyevolution of the sample are consistent with the predictions of spherical phaseshock-cooling (SC), independently of the presence of `flash ionization"features. We present a framework for fitting SC models which can reproduce theparameters of a set of multi-group simulations without a significant bias up to20% in radius and velocity. Observations of about half of the SNe II in thesample are well-fit by models with breakout radii $<10^{14}\,$cm. The otherhalf are typically more luminous, with observations from day 1 onward that arebetter fit by a model with a large $>10^{14}\,$cm breakout radius. However,these fits predict an early rise during the first day that is too slow. Wesuggest these large-breakout events are explosions of stars with an inflatedenvelope or a confined CSM with a steep density profile, at which breakoutoccurs. Using the X-ray data, we derive constraints on the extended($\sim10^{15}$ cm) CSM density independent of spectral modeling, and find mostSNe II progenitors lose $<10^{-4} M_{\odot}\, \rm yr^{-1}$ a few years beforeexplosion. This provides independent evidence the CSM around many SNe IIprogenitors is confined. We show that the overall observed breakout radiusdistribution is skewed to higher radii due to a luminosity bias. We argue thatthe $66^{+11}_{-22}\%$ of red supergiants (RSG) explode as SNe II with breakoutradii consistent with the observed distribution of field RSG, with a tailextending to large radii, likely due to the presence of CSM.

The Early Ultraviolet Light-Curves of Type II Supernovae and the Radii of Their Progenitor Stars