  We present $\simeq$0$.\!\!^{\prime\prime}4$-resolution extinction-independent
distributions of star formation and dust in 11 star-forming galaxies (SFGs) at
$z = 1.3-3.0$. These galaxies are selected from sensitive, blank-field surveys
of the $2' \times 2'$ Hubble Ultra-Deep Field at $\lambda = 5$ cm and 1.3 mm
using the Karl G. Jansky Very Large Array (VLA) and Atacama Large
Millimeter/submillimeter Array (ALMA). They have star-formation rates (SFRs),
stellar masses, and dust properties representative of massive main-sequence
SFGs at $z \sim 2$. Morphological classification performed on
spatially-resolved stellar mass maps indicates a mixture of disk and
morphologically disturbed systems; half of the sample harbor X-ray active
galactic nuclei (AGN), thereby representing a diversity of $z \sim 2$ SFGs
undergoing vigorous mass assembly. We find that their intense star formation
most frequently occurs at the location of stellar-mass concentration and
extends over an area comparable to their stellar-mass distribution, with a
median diameter of $4.2 \pm 1.8$ kpc. This provides direct evidence for
galaxy-wide star formation in distant, blank-field-selected main-sequence SFGs.
The typical galactic-average SFR surface density is 2.5
M$_{\odot}$yr$^{-1}$kpc$^{-2}$, sufficiently high to drive outflows. In
X-ray-selected AGN where radio emission is enhanced over the level associated
with star formation, the radio excess pinpoints the AGN, which are found to be
co-spatial with star formation. The median extinction-independent size of
main-sequence SFGs is two times larger than those of bright submillimeter
galaxies whose SFRs are $3-8$ times larger, providing a constraint on the
characteristic SFR ($\sim300$ M$_{\odot}$yr$^{-1}$) above which a significant
population of more compact star-forming galaxies appears to emerge.
