The IllustrisTNG project is a new suite of cosmological magneto-hydrodynamical simulations of galaxy formation performed with the Arepo code and updated models for feedback physics. Here we introduce the first two simulations of the series, TNG100 and TNG300, and quantify the stellar mass content of about 4000 massive galaxy groups and clusters ($10^{13} leq M_{rm 200c}/M_{rm sun} leq 10^{15}$) at recent times ($z leq 1$). The richest clusters have half of their total stellar mass bound to satellite galaxies, with the other half being associated with the central galaxy and the diffuse intra-cluster light. The exact ICL fraction depends sensitively on the definition of a central galaxys mass and varies in our most massive clusters between 20 to 40% of the total stellar mass. Haloes of $5times 10^{14}M_{rm sun}$ and above have more diffuse stellar mass outside 100 kpc than within 100 kpc, with power-law slopes of the radial mass density distribution as shallow as the dark matters ( $-3.5 < alpha_{rm 3D} < -3$). Total halo mass is a very good predictor of stellar mass, and vice versa: at $z=0$, the 3D stellar mass measured within 30 kpc scales as $propto (M_{rm 500c})^{0.49}$ with a $sim 0.12$ dex scatter. This is possibly too steep in comparison to the available observational constraints, even though the abundance of TNG less massive galaxies ($< 10^{11}M_{rm sun}$ in stars) is in good agreement with the measured galaxy stellar mass functions at recent epochs. The 3D sizes of massive galaxies fall too on a tight ($sim$0.16 dex scatter) power-law relation with halo mass, with $r^{rm stars}_{rm 0.5} propto (M_{rm 500c})^{0.53}$. Even more fundamentally, halo mass alone is a good predictor for the whole stellar mass profiles beyond the inner few kpc, and we show how on average these can be precisely recovered given a single mass measurement of the galaxy or its halo.
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