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There is still much debate surrounding how the most massive, central galaxiesin the local universe have assembled their stellar mass, especially therelative roles of in-situ growth versus later accretion via mergers. In thispaper, we set firmer constraints on the evolutionary pathways of the mostmassive central galaxies by making use of empirical estimates on theirabundances and stellar ages. The most recent abundance matching and directmeasurements strongly favour that a substantial fraction of massive galaxieswith Mstar>3x10^11 Msun reside at the centre of clusters with massMhalo>3x10^13 Msun. Spectral analysis supports ages >10 Gyrs, corresponding toa formation redshift z_form >2. We combine these two pieces ofobservationally-based evidence with the mass accretion history of their hostdark matter haloes. We find that in these massive haloes, the stellar masslocked up in the central galaxy is comparable to, if not greater than, thetotal baryonic mass at z_form. These findings indicate that either only arelatively minor fraction of their present-day stellar mass was formed in-situat z_form, or that these massive, central galaxies form in the extreme scenariowhere almost all of the baryons in the progenitor halo are converted intostars. Interestingly, the latter scenario would not allow for any substantialsize growth since the galaxy's formation epoch either via mergers or expansion.We show our results hold irrespective of systematic uncertainties in stellarmass, abundances, galaxy merger rates, stellar initial mass function, starformation rate and dark matter accretion histories.

Setting firmer constraints on the evolution of the most massive, central galaxies from their local abundances and ages