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We use the TNG100 simulation of the IllustrisTNG project to investigate thestellar specific angular momenta ($j_{\ast}$) of $\sim$12,000 central galaxiesat $z=0$ 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 inIllustrisTNG are in good overall agreement with observations, and that thesegalaxy types typically `retain' $\sim$10-20 and $\sim$50-60 per cent of theirhost haloes' specific angular momenta, respectively, with some dependence onthe methodology used to measure galaxy morphology. We present results forkinematic as well as visual-like morphological measurements of the simulatedgalaxies. Next, we explore the scatter in the $j_{\ast}$-$M_{\ast}$ relationwith respect to the spin of the dark matter halo and the mass of thesupermassive black hole (BH) at the galactic centre. We find that galaxiesresiding 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 fixedgalaxy 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 centrein slowly rotating systems. Finally, we show that halo spin plays an importantrole in determining galaxy sizes - larger discs form at the centres offaster-rotating haloes - although the trend breaks down for massive galaxieswith $M_{\ast} \gtrsim 10^{11} \, {\rm M}_{\odot}$, roughly the mass scale atwhich a galaxy's stellar mass becomes dominated by accreted stars.

Galactic angular momentum in the IllustrisTNG simulation -- I. Connection to morphology, halo spin, and black hole mass