The Progenitors of Local Ultra-massive Galaxies Across Cosmic Time: from
  Dusty Star-bursting to Quiescent Stellar Populations
  Using the UltraVISTA catalogs, we investigate the evolution in the 11.4~Gyr
since $z=3$ of the progenitors of local ultra-massive galaxies ($\log{(M_{\rm
star}/M_{\odot})}\approx11.8$; UMGs), providing a complete and consistent
picture of how the most massive galaxies at $z=0$ have assembled. By selecting
the progenitors with a semi-empirical approach using abundance matching, we
infer a growth in stellar mass of 0.56$^{+0.35}_{-0.25}$ dex,
0.45$^{+0.16}_{-0.20}$~dex, and 0.27$^{+0.08}_{-0.12}$ dex from $z=3$, $z=2$,
and $z=1$, respectively, to $z=0$. At $z<1$, the progenitors of UMGs constitute
a homogeneous population of only quiescent galaxies with old stellar
populations. At $z>1$, the contribution from star-forming galaxies
progressively increases, with the progenitors at $2<z<3$ being dominated by
massive ($M_{\rm star} \approx 2 \times 10^{11}$M$_{\odot}$), dusty ($A_{\rm
V}\sim$1--2.2 mag), star-forming (SFR$\sim$100--400~M$_{\odot}$ yr$^{-1}$)
galaxies with a large range in stellar ages. At $z=2.75$, $\sim$15\% of the
progenitors are quiescent, with properties typical of post-starburst galaxies
with little dust extinction and strong Balmer break, and showing a large
scatter in color. Our findings indicate that at least half of the stellar
content of local UMGs was assembled at $z>1$, whereas the remaining was
assembled via merging from $z\sim 1$ to the present. Most of the quenching of
the star-forming progenitors happened between $z=2.75$ and $z=1.25$, in good
agreement with the typical formation redshift and scatter in age of $z=0$ UMGs
as derived from their fossil records. The progenitors of local UMGs, including
the star-forming ones, never lived on the blue cloud since $z=3$. We propose an
alternative path for the formation of local UMGs that refines previously
proposed pictures and that is fully consistent with our findings.
