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.

14 pages, 9 figures. MNRAS Accepted. Minor changes after referee report