case 50), and $m_{\rm part}$ is the mass of an SPH particle. The 150 Pop. III.2 simulations have a mass resolution of 0.008 . Once the candidate particle has passed the criteria described in Bate et al. (1995), it is replaced by a sink particle that can accrete gas particles that fall within its accretion radius $r_{\rm acc}$, which we fix at 20 AU. Note that this radius is significantly larger than the Jeans radius at the point that the gas reaches the density threshold for sink creation, which is around 6 AU. As such, all the fragmentation that we capture in this study is well resolved and not lying close to the limits of our resolution; if any ‘artificial’ fragmentation were to occur, the sink particle would immediately swallow the offending region and replace it with a single accreting point. We also prevent sink particles from forming within $2\, r_{\rm acc}$ of one another. This prevents the formation of sinks out of gas that in reality would by accreted by a neighboring sink particle before it could go into direct collapse by itself. Lastly, gravitational interactions between sinks, and between the sinks and the gas, are softened in the 