© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. 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 J21and 1000 J21, respectively, we construct environments conducive to the formation of massive stars. We find that only in the case of the higher LW backgrounds supercritical accretion rates are realized that are necessary for supermassive star formation. Mild fragmentation is observed for both backgrounds. Violent dynamical interactions between the stars that form in the more massive halo formed (1000 J21background) results in the eventual expulsion of the twomostmassive stars from the halo. In the smallermass halo (100 J21background) mergers of stars occur before any multibody interactions and a single massive Population III star is left at the centre of the halo at the end of our simulation. Feedback from the very massive Population III stars is not effective in generating a large H II region with ionizing 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 Population III star which remained at the centre of the less massive halo experiences steady accretion rates of almost 10-2M⊙yr-1and if these rates continue it could potentially experience super-Eddington accretion rates in the immediate aftermath of collapsing into a black hole.