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The evolution of the stellar mass-size relation of bulges and disks since $z = 1$

We explore the evolution of the stellar mass-size relation of galaxies of different morphological types and specifically bulge and disk components. We use a sample of $\sim35,000$ galaxies within a redshift range $0 < z < 1$, and stellar mass $\log_{10}(\mathrm{M}_*/\mathrm{M}_\odot) \geq 9.5$ volume-limited sample drawn from the combined DEVILS and HST-COSMOS region for which we presented a morphological classification into sub-classes of double-component (BD), pure-disk (pD), elliptical (E), and compact (C) in Paper-I and a structural decomposition into disk (D), diffuse bulge (dB), and compact bulge (cB) in Paper-II. We find that compared to disks, ellipticals and bulges follow steeper $M_*-R_e$ relations, likely indicating distinct evolutionary mechanisms. Ellipticals and disk structures follow consistently unchanged slopes of $\sim0.5$ and $\sim0.3$, respectively, at all redshifts. We quantify that disks follow a redshift independent $M_*-R_e$ slope regardless of the presence or absence of a bulge component (i.e., BD or pD) suggesting a similar origin and evolutionary pathway for all disks. Since $z = 1$ compact-bulges present a steepening relation which do not follow that of Es whilst diffuse-bulges experience a modest flattening. Overall, we find a close-to-no variation in the $M_*-R_e$ relations over the last $\sim8$ Gyr suggesting that despite ongoing although declining star-formation, mass evolution, morphological transitions and mergers, evolution moves galaxies along their $M_*-R_e$ trails. This seems to be consistent with an inside-out growth and evolution picture in which galaxies grow in size as they do in stellar mass. Besides, minor mergers are likely to be responsible for the growth of Es, at least in $z < 1$.