  We analyze the size evolution of $16000$ star-forming galaxies (SFGs) and
$5000$ quiescent galaxies (QGs) with mass $M_*>10^{9.5}M_\odot$ at $0.1<z<0.9$
from the COSMOS field using deep CLAUDS+HSC imaging in two rest-frame
wavelengths, $3000$\r{A} (UV light) and $5000$\r{A} (visible light). With
half-light radius ($R_e$) as proxy for size, SFGs at characteristic mass $M_0 =
5\times10^{10}M_\odot$ grow by $20\%$ ($30\%$) in UV (visible) light since
$z\sim1$ and the strength of their size evolution increases with stellar mass.
After accounting for mass growth due to star formation, we estimate that SFGs
grow by $75\%$ in all stellar mass bins and in both rest-frame wavelengths.
Redder SFGs are more massive, smaller and more concentrated than bluer SFGs and
the fraction of red SFGs increases with time. These results point to the
emergence of bulges as the dominant mechanism for the average size growth of
SFGs. We find two threshold values for the stellar mass density within central
$1$kpc (${\Sigma}_1$): all SFGs with $\log{\Sigma}_1 > 9$ are red and only QGs
have $\log{\Sigma}_1>9.7$. The size of $M_*=M_0$ QGs grows by $50\%$ ($110\%$)
in the UV (visible) light. Up to $\sim20\%$ of this increase in size of massive
QGs is due to newcomers (recently quenched galaxies). However, newcomers cannot
explain the observed pace in the size growth of QGs; that trend has to be
dominated by processes affecting individual galaxies, such as minor mergers and
accretion.
