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We discuss how the effective radius  R  e  function (ERF) recently worked out by Bernardi et al. represents a new testbed to improve the current understanding of semi‐analytic models of galaxy formation. In particular, we show here that a detailed hierarchical model of structure formation can broadly reproduce the correct peak in the size distribution of local early‐type galaxies, although it significantly overpredicts the number of very compact and very large galaxies. This in turn is reflected in the predicted size–mass relation, much flatter than the observed one, due to too large (≳3 kpc) low‐mass galaxies  (&lt;10 11  M ⊙ ) , and to a non‐negligible fraction of compact  (≲0.5–1 kpc)  and massive galaxies  (≳10 11  M ⊙ ) . We also find that the latter discrepancy is smaller than previously claimed, and limited to only ultra‐compact ( R  e   ≲ 0.5 kpc ) galaxies when considering elliptical‐dominated samples. We explore several causes behind these effects. We conclude that the former problem might be linked to the initial conditions, given that large and low‐mass galaxies are present at all epochs in the model. The survival of compact and massive galaxies might instead be linked to their very old ages and peculiar merger histories. Overall, knowledge of the galactic stellar mass  and  size distributions allows a better understanding of where and how to improve models.

Further constraining galaxy evolution models through the size function of SDSS early‐type galaxies