  We analyze scaling relations and evolution histories of galaxy sizes in
TNG100, part of the IllustrisTNG simulation suite. Observational qualitative
trends of size with stellar mass, star-formation rate and redshift are
reproduced, and a quantitative comparison of projected r-band sizes at 0~<z<~2
shows agreement to much better than 0.25dex. We follow populations of z=0
galaxies with a range of masses backwards in time along their main progenitor
branches, distinguishing between main-sequence and quenched galaxies. Our main
findings are as follows. (i) At M_{*,z=0}>~10^{9.5}Msun, the evolution of the
median main progenitor differs, with quenched galaxies hardly growing in median
size before quenching, whereas main-sequence galaxies grow their median size
continuously, thus opening a gap from the progenitors of quenched galaxies.
This is partly because the main-sequence high-redshift progenitors of quenched
z=0 galaxies are drawn from the lower end of the size distribution of the
overall population of main-sequence high-redshift galaxies. (ii) Quenched
galaxies with M_{*,z=0}>~10^{9.5}Msun experience a steep size growth on the
size-mass plane after their quenching time, but with the exception of galaxies
with M_{*,z=0}>~10^{11}Msun, the size growth after quenching is small in
absolute terms, such that most of the size (and mass) growth of quenched
galaxies (and its variation among them) occurs while they are still on the
main-sequence. After they become quenched, the size growth rate of quenched
galaxies as a function of time, as opposed to versus mass, is similar to that
of main-sequence galaxies. Hence, the size gap is retained down to z=0.
