The stellar mass assembly of galaxies can be affected by both secular and environmental processes. In this study, for the first time, we investigate the stellar mass assembly of $sim90,000$ low redshift, central galaxies selected from SDSS group catalogues (M$_{rm Stellar}gtrsim10^{9.5}$M$_{odot}$, M$_{rm Halo}gtrsim10^{12}$M$_{odot}$) as a function of both stellar and halo mass. We use estimates of the times at which 10, 50 and 90 per cent of the stellar mass was assembled from photometric spectral energy distribution fitting, allowing a more complete investigation than single stellar ages alone. We consider trends in both stellar and halo mass simultaneously, finding dependencies of all assembly times on both. We find that galaxies with higher stellar masses (at constant halo mass) have on average older lookback times, similar to previous studies of galaxy assembly. We also find that galaxies at higher halo mass (at constant stellar mass) have younger lookback times, possibly due to a larger reservoir of gas for star formation. An exception to this is a sub sample with high stellar-to-halo mass ratios, which are likely massive, field spirals. We compare these observed trends to those predicted by the TNG300 simulation, finding good agreement overall as a function of either stellar or halo mass. However, some differences in the assembly times (of up to $sim 3$ Gyr) appear when considering both stellar and halo mass simultaneously, noticeably at intermediate stellar masses (M$_{rm Stellar} sim 10^{11}$ M$_{odot}$). These discrepancies are possibly linked to the quenched fraction of galaxies and the kinetic mode AGN feedback implemented in TNG300.
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