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