  We use high resolution adaptive mesh refinement simulations to model the
formation of massive metal-free stars in the early Universe. By applying
Lyman-Werner (LW) backgrounds of 100 J$_{21}$ and 1000 J$_{21}$ respectively we
construct environments conducive to the formation of massive stars. We find
that only in the case of the higher LW backgrounds are super-critical accretion
rates realised that are necessary for super-massive star (SMS) formation. Mild
fragmentation is observed for both backgrounds. Violent dynamical interactions
between the stars that form in the more massive halo formed (1000 J$_{21}$
background) results in the eventual expulsion of the two most massive stars
from the halo. In the smaller mass halo (100 J$_{21}$ background) mergers of
stars occur before any multibody interactions and a single massive Pop III star
is left at the centre of the halo at the end of our simulation. Feedback from
the very massive Pop III stars is not effective in generating a large HII
region with ionising photons absorbed within a few thousand AU of the star. In
all cases a massive black hole seed is the expected final fate of the most
massive objects. The seed of the massive Pop III star which remained at the
centre of the less massive halo experiences steady accretion rates of almost
$10^{-2}$ M$_{\odot}$/yr and if these rates continue could potentially
experience super-Eddington accretion rates in the immediate aftermath of
collapsing into a black hole.
