The intrinsic sizes of the field galaxies with I \leq 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 \sim 0.5 .
The excess persists up to z \sim 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 .