  We use the TNG100 simulation of the IllustrisTNG project to investigate the
stellar specific angular momenta ($j_{\ast}$) of $\sim$12,000 central galaxies
at $z=0$ in a full cosmological context, with stellar masses ($M_{\ast}$)
ranging from $10^{9}$ to $10^{12} \, {\rm M}_{\odot}$. We find that the
$j_{\ast}$-$M_{\ast}$ relations for early-type and late-type galaxies in
IllustrisTNG are in good overall agreement with observations, and that these
galaxy types typically `retain' $\sim$10-20 and $\sim$50-60 per cent of their
host haloes' specific angular momenta, respectively, with some dependence on
the methodology used to measure galaxy morphology. We present results for
kinematic as well as visual-like morphological measurements of the simulated
galaxies. Next, we explore the scatter in the $j_{\ast}$-$M_{\ast}$ relation
with respect to the spin of the dark matter halo and the mass of the
supermassive black hole (BH) at the galactic centre. We find that galaxies
residing in faster spinning haloes, as well as those hosting less massive BHs,
tend to have a higher specific angular momentum. We also find that, at fixed
galaxy or halo mass, halo spin and BH mass are anticorrelated with each other,
probably as a consequence of more efficient gas flow toward the galactic centre
in slowly rotating systems. Finally, we show that halo spin plays an important
role in determining galaxy sizes - larger discs form at the centres of
faster-rotating haloes - although the trend breaks down for massive galaxies
with $M_{\ast} \gtrsim 10^{11} \, {\rm M}_{\odot}$, roughly the mass scale at
which a galaxy's stellar mass becomes dominated by accreted stars.
