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ABSTRACT We use the improved IllustrisTNG300 magnetohydrodynamical cosmological simulation to revisit the effect that secondary halo bias has on the clustering of the central galaxy population. With a side length of 205 h−1 Mpc and significant improvements on the subgrid model with respect to previous Illustris simulations, IllustrisTNG300 allows us to explore the dependencies of galaxy clustering over a large cosmological volume and halo mass range. We show at high statistical significance that the halo assembly bias signal (i.e. the secondary dependence of halo bias on halo formation redshift) manifests itself on the clustering of the galaxy population when this is split by stellar mass, colour, specific star formation rate, and surface density. A significant signal is also found for galaxy size: at fixed halo mass, larger galaxies are more tightly clustered than smaller galaxies. This effect, in contrast to the rest of the dependencies, seems to be uncorrelated with halo formation time, with some small correlation only detected for halo spin. We also explore the transmission of the spin bias signal, i.e. the secondary dependence of halo bias on halo spin. Although galaxy spin retains little information about the total halo spin, the correlation is enough to produce a significant galaxy spin bias signal. We discuss possible ways to probe this effect with observations.