  Using the SMUDGes and SDSS catalogs, and our own reprocessing of the Legacy
Surveys imaging, we investigate the properties of nuclear star clusters (NSCs)
in galaxies having central surface brightnesses as low as 27 mag arcsec$^{-2}$.
We identify 273 (123 with known redshift) and 32 NSC-bearing galaxies in the
two samples, respectively, where we require candidate NSCs to have a separation
of less than 0.10$r_e$ from the galaxy center. We find that galaxies with low
central surface brightness ($\mu_{0,g} > 24$ mag arcsec$^{-2}$) are more likely
to contain an NSC if 1) they have a higher stellar mass, 2) a higher stellar to
total mass ratio, 3) a brighter central surface brightness, 4) a larger axis
ratio, or 5) lie in a denser environment. Because of the correlations among
these various quantities, it is likely that only one or two are true physical
drivers. We also find scaling relations for the NSC mass with stellar mass
($M_{NSC}/$\Msol$ = 10^{6.02\pm0.03}(M_{*,gal}/10^{8} $\Msol$)^{0.77\pm0.04}$)
and halo mass ($M_{NSC}/$\Msol$ = 10^{6.11\pm0.05}(M_{h,gal}/10^{10}
$\Msol$)^{0.92\pm0.05}$), although it is the scaling with halo mass that is
consistent with a direct proportionality. In galaxies with an NSC, $M_{NSC}
\approx 10^{-4}M_{h,gal}$. This proportionality echoes the finding of a direct
proportionality between the mass (or number) of globular clusters (GCs) in
galaxies and the galaxy's total mass. These findings favor a related origin for
GCs and NSCs.
