  We present a new cosmological, magnetohydrodynamical simulation for galaxy
formation: TNG50, the third and final installment of the IllustrisTNG project.
TNG50 evolves 2x2160^3 dark-matter particles and gas cells in a volume 50
comoving Mpc across. It hence reaches a numerical resolution typical of zoom-in
simulations, with a baryonic element mass of 8.5x10^4 Msun and an average cell
size of 70-140 parsecs in the star-forming regions of galaxies. Simultaneously,
TNG50 samples ~700 (6,500) galaxies with stellar masses above 10^10 (10^8) Msun
at z=1. Here we investigate the structural and kinematical evolution of
star-forming galaxies across cosmic time (0 < z < 6). We quantify their sizes,
disk heights, 3D shapes, and degree of rotational vs. dispersion-supported
motions as traced by rest-frame V-band light (i.e. roughly stellar mass) and by
Halpha light (i.e. star-forming and dense gas). The unprecedented resolution of
TNG50 enables us to model galaxies with sub-kpc half-light radii and with
<300-pc disk heights. Coupled with the large-volume statistics, we characterize
a diverse, redshift- and mass-dependent structural and kinematical
morphological mix of galaxies all the way to early epochs. Our model predicts
that for star-forming galaxies the fraction of disk-like morphologies, based on
3D stellar shapes, increases with both cosmic time and galaxy stellar mass. Gas
kinematics reveal that the vast majority of 10^9-11.5 Msun star-forming
galaxies are rotationally-supported disks for most cosmic epochs
(Vmax/sigma>2-3, z<5), being dynamically hotter at earlier epochs (z>1.5).
Despite large velocity dispersion at high redshift, cold and dense gas in
galaxies predominantly arranges in disky or elongated shapes at all times and
masses; these gaseous components exhibit rotationally-dominated motions far
exceeding the collisionless stellar bodies.
