We present a suite of six fully cosmological, three-dimensional simulations of the collapse of an atomic cooling halo in the early Universe. We use the moving-mesh code arepo with an improved primordial chemistry network to evolve the hydrodynamical and chemical equations. The addition of a strong Lyman-Werner background suppresses molecular hydrogen cooling and permits the gas to evolve nearly isothermally at a temperature of about 8000 K. Strong gravitational torques effectively remove angular momentum and lead to the central collapse of gas, forming a supermassive protostar at the center of the halo. We model the protostar using two methods: sink particles that grow through mergers with other sink particles, and a stiff equation of state that leads to the formation of an adiabatic core. We impose threshold densities of 10 8 , 10 10 , and 10 12 cm −3 for the sink particle formation and the onset of the stiff equation of state to study the late, intermediate, and early stages in the evolution of the protostar, respectively. We follow its growth from masses 10 M to 10 5 M , with an average accretion rate of M 2 M yr −1 for sink particles, and 0.8−1.4 M yr −1 for the adiabatic cores. At the end of the simulations, the Hii region generated by radiation from the central object has long detached from the protostellar photosphere, but the ionizing radiation remains trapped in the inner host halo, and has thus not yet escaped into the intergalactic medium. Fully coupled, radiation-hydrodynamics simulations hold the key for further progress.