  The dense environment of galaxy clusters strongly influences the nature of
galaxies. Here, we study the cause of the size distribution of a sample of 560
spectroscopic members spanning a wide dynamical range down to 10^8.5 M_sol
(log(M)-2) in the massive CLASH cluster MACSJ 1206.2-0847 at z~0.44. We use
Subaru SuprimeCam imaging covering the highest-density core out to the infall
regions (3 virial radii) to look for cluster-specific effects. We also compare
our measurements to a compatible large field study in order to span extreme
environmental densities. This paper presents the trends we identified for
cluster galaxies divided by their colors into star-forming and quiescent
galaxies and into distinct morphological types (using S\'ersic index and
bulge/disk decompositions). We observed larger sizes for early type and smaller
sizes for massive late type galaxies in clusters in comparison to the field. We
attribute this to longer quenching timescales of more massive galaxies in the
cluster. Our analysis further revealed an increasing importance of recently
quenched transition objects ("red disks"). This is a virialized population
found at higher cluster-centric radii with sizes similar to the quiescent,
spheroid-dominated population of the cluster center, but with disks still
in-tact. The mass-size relation of cluster galaxies may therefore be understood
as the consequence of a mix of progenitors formed at different quenching
epochs. We also find that galaxy sizes smoothly decreasing as a function of
bulge fraction. At same bulge-to-total ratio and same stellar mass, quiescent
galaxies are smaller than star-forming galaxies. This is likely because of a
fading of the outskirts of the disk, which we saw in comparing sizes of their
disk-components. Ram-pressure stripping of the cold gas and other forms of more
gradual gas starvation are likely responsible for this observation.
