Comparing the Evolution of the Galaxy Disk Sizes with CDM Models: The   Hubble Deep Field
  The intrinsic sizes of the field galaxies with I<26 in the Hubble and ESO-NTT Deep Fields are shown as a function of their redshifts and absolute magnitudes using photometric redshifts derived from the multicolor catalogs and are compared with the CDM predictions. Extending to lower luminosities and to higher z our previous analysis performed on the NTT field alone, we find that the distribution of the galaxy disk sizes at different cosmic epochs is within the range predicted by typical CDM models. However, the observed size distribution of faint (M_B>-19) galaxies is skewed with respect to the CDM predictions and an excess of small-size disks (R_d<2 kpc) is already present at z~ 0.5. The excess persists up to z~3 and involves brighter galaxies . Such an excess may be reduced if luminosity-dependent effects, like starburst activity in interacting galaxies, are included in the physical mechanisms governing the star formation history in CDM models. 
E. Giallongo, N. Menci, F. Poli, S. D'Odorico, A. Fontana