  Supermassive stars forming at $z \sim$ 15 - 20 are one of the leading
contenders for the origin of the first quasars, over 200 of which have now been
discovered at $z >$ 6. These stars likely form in pristine, atomically cooled
haloes immersed in strong Lyman-Werner UV backgrounds or in highly supersonic
baryon streaming flows. Atomic cooling triggers catastrophic baryon collapse
capable of building up stars at rates of up to $\sim$1 M$_{\odot}$ yr$^{-1}$.
Here we examine the evolution of supermassive stars with a much larger and
finer grid of accretion rates than in previous studies with the \texttt{MESA}
stellar evolution code. We find that their final masses range from 3.5 $\times$
10$^3$ M$_{\odot}$ - 3.7 $\times$ 10$^5$ M$_{\odot}$ at accretion rates of
0.001 M$_{\odot}$ yr$^{-1}$ - 1 M$_{\odot}$ yr$^{-1}$, respectively. We also
find that supermassive star evolution diverges at accretion rates of 0.01
M$_{\odot}$ yr$^{-1}$ - 0.02 M$_{\odot}$ yr$^{-1}$, above which they evolve as
cool red hypergiants along the Hayashi track and collapse via the general
relativistic instability during central hydrogen burning, and below which they
evolve as hot blue supergiants and collapse at the end of their nuclear burning
lifetimes after exiting the main sequence.
