Cumulative distribution of final core masses, M_He, preSN, of Type II SN progenitors. White squares are the inferred core mass or upper limits of observed SN II progenitors from Smartt (2015). For comparison we show our predicted cumulative distribution for progenitors that evolved as single stars (black dashed line) or including possible binary interactions (red solid line), following our standard assumptions. The equivalent single-star initial mass, M_ZAMS, corresponding to each M_He, preSN is shown on the top x-axis. The equivalent pre-SN progenitor luminosity, corresponding to each M_He, preSN value according to single STARS models which were also used in Smartt et al. (2009), is shown on the bottom x-axis. We also show the range of uncertainty (red-shaded region with white dashed lines) of the expected distributions found for our simulated populations in which we vary the treatment of binary physics. These include among others the efficiency of mass transfer and of common envelope evolution, the initial period and mass ratio distribution and the binary fraction.