  Physical and chemical properties of the interstellar medium (ISM) at
sub-galactic ($\sim$kpc) scales play an indispensable role in controlling the
ability of gas to form stars. As part of the SMAUG (Simulating Multiscale
Astrophysics to Understand Galaxies) project, in this paper, we use the TNG50
cosmological simulation to explore the physical parameter space of 8 resolved
ISM properties in star-forming regions to constrain the areas of this
hyperspace over which most star-forming environments exist. We deconstruct our
simulated galaxies spanning a wide range of mass (M$_\star = 10^{7-11}$
M$_\odot$) and redshift ($0 \leq z \leq 3$) into kpc-sized regions, and
statistically analyze the gas/stellar surface densities, gas metallicity,
vertical stellar velocity dispersion, epicyclic frequency and dark-matter
volumetric density representative of each region in the context of their star
formation activity and galactic environment (radial galactocentric location).
By examining the star formation rate (SFR) weighted distributions of these
properties, we show that stars primarily form in two spatially distinct
environmental regimes, which are brought about by an underlying bi-component
radial SFR surface density profile in galaxies. We examine how the relative
prominence of these two regimes depends on host galaxy mass and cosmic time. We
also compare our findings with those from integral field spectroscopy
observations and achieve a good overall agreement. Further, using
dimensionality reduction, we characterise the aforementioned hyperspace to
reveal a high-degree of multicollinearity in relationships amongst ISM
properties that drive the distribution of star formation at kpc-scales. Based
on this, we show that a reduced 3D representation underpinned by a
multi-variate radius relationship is sufficient to capture most of the variance
in the original 8D space.
