  The size-mass galaxy distribution is a key diagnostic for galaxy evolution.
Massive compact galaxies are potential surviving relics of a high-redshift
phase of star formation. Some of these could be nearly unresolved in SDSS
imaging and thus not included in galaxy samples. To overcome this, a sample was
selected from the combination of SDSS and UKIDSS photometry to r<17.8. This was
done using colour-colour selection, and then by obtaining accurate photometric
redshifts (photo-z) using scaled flux matching (SFM). Compared to spectroscopic
redshifts (spec-z), SFM obtained a 1-sigma scatter of 0.0125 with only 0.3%
outliers (Delta:ln(1+z)>0.06). A sample of 163186 galaxies was obtained with
0.04<z<0.15 over 2300 sq.deg. using a combination of spec-z and photo-z.
Following Barro et al., log:Sigma_1.5=log:M_*-1.5log:reff was used to define
compactness. The spectroscopic completeness was 76% for compact galaxies
(log:Sigma_1.5>10.5) compared to 92% for normal-size galaxies. This difference
is primarily attributed to SDSS `fibre collisions' and not the completeness of
the main galaxy sample selection. Using environmental overdensities, this
confirms that compact quiescent galaxies are significantly more likely to be
found in high-density environments compared to normal-size galaxies. By
comparison with a high-redshift sample from 3D-HST, log:Sigma_1.5 distribution
functions show significant evolution, with this being a compelling way to
compare with simulations such as EAGLE. The number density of compact quiescent
galaxies drops by a factor of about 30 from z~2 to log(n/Mpc^-3)=-5.3+-0.4 in
the SDSS-UKIDSS sample. The uncertainty is dominated by the steep cut off in
log:Sigma_1.5, which is demonstrated conclusively using this complete sample.
