  Primordial supermassive stars (SMSs) formed in atomic-cooling halos at z ~ 15
- 20 are leading candidates for the seeds of the first quasars. Past numerical
studies of the evolution of SMSs have typically assumed constant accretion
rates rather than the highly variable flows in which they form. We model the
evolution of SMSs in the cosmological flows that create them using the Kepler
stellar evolution and implicit hydrodynamics code. We find that they reach
masses of 1 - 2 x $10^5 M_{\odot}$ before undergoing direct-collapse to black
holes (DCBHs) during or at the end of their main-sequence hydrogen burning, at
1 - 1.5 Myr, regardless of halo mass, spin, or merger history. We also find
that realistic, highly-variable accretion histories allow for a much greater
diversity of supermassive stellar structures, including in some cases largely
thermally relaxed objects, which may provide a significant source of radiative
feedback. Our models indicate that the accretion histories predicted for purely
atomic-cooling halos may impose a narrow spectrum of masses on the seeds of the
first massive quasars, however further studies incorporating realistic feedback
will be essential in order to confirm whether or not this holds true in all
cases. Our results also indicate that multiple SMSs at disparate stages of
evolution can form in these halos, raising the possibility of SMS binaries and
supermassive X-ray binaries (SMXBs), as well as DCBH mergers which could be
detected by LISA.
