  Measurements of the dependence of stellar specific angular momentum ($j_*$)
on stellar mass ($M_*$) are presented for large samples of ALFALFA galaxies
spanning the stellar mass range $\sim 10^8$-$10^{11}$ M$_{\odot}$. Accurate
estimates of $j_*$ are generated using measurements of $I$-band effective
radius and velocity width of the HI line profile. While the full sample
($N=3~607)$ of galaxies yields a $j_*$-$M_*$ relation with power-law index
$\alpha = 0.404\pm 0.03$, it is shown that various sub-samples have indices
that are very similar to the best literature results, yet with comparatively
lower intrinsic scatters. A galaxy's mean $I$-band surface brightness within
its effective radius ($<\mu_\mathrm{eff}>$) is shown to significantly correlate
with $j_*$-$M_*$ scatter. A 3D plane fit to all $N=3~607$ galaxies in
$\log_{10}j_*$-$\log_{10}M_*$-$<\mu_\mathrm{eff}>$ space yields $j_*\propto
M_*^{0.589\pm 0.002}<\mu_\mathrm{eff}>^{0.193\pm 0.002}$ with scatter
$\sigma=0.089$ dex. $<\mu_\mathrm{eff}>$-selected sub-samples of size up to
$N=1~450$ yield power-law $j_*$-$M_*$ relations mostly consistent with
$\alpha=0.55\pm 0.02$ from the literature and with intrinsic scatter ranging
from 0.083 to 0.129 dex. Thus, this paper presents new, highly accurate
measurements of the $j_*$-$M_*$ relation that can be used to better understand
the important roles played by angular momentum in the formation and evolution
of galaxies.
