We demonstrate the formation of gravitationally unstable discs in magnetized molecular cloud cores with initial mass-to-flux ratios of five times the critical value, effectively solving the magnetic braking catastrophe. We model the gravitational collapse through to the formation of the stellar core, using Ohmic resistivity, ambipolar diffusion and the Hall effect, and using the canonical cosmic ray ionization rate of ζcr = 10−17 s−1. When the magnetic field and rotation axis are initially aligned, a ≲ 1 au disc forms after the first core phase, whereas when they are anti-aligned, a gravitationally unstable 25 au disc forms during the first core phase. The aligned model launches a 3 km s−1 first core outflow, while the anti-aligned model launches only a weak ≲ 0.3 km s−1 first core outflow. Qualitatively, we find that models with ζcr = 10−17 s−1 are similar to purely hydrodynamical models if the rotation axis and magnetic field are initially anti-aligned, whereas they are qualitatively similar to ideal magnetohydrodynamical models if initially aligned.,This is the data created for Wurster, Bate & Price (2018c): Hall effect-driven formation of gravitationally unstable discs in magnetized molecular cloud cores. This dataset was created using the smoothed particle magnetohydrodynamics code sphNG, which included v1.2.1 of the NICIL library (Wurster 2016) to calculate the non-ideal MHD coefficients. The raw data and important files have been uploaded; the data files can be read with either sphNG, or with the graphics programme Splash (Price 2007). The file are named such that number at the end of `collapse' indicates the negative of the cosmic ray ionisation rate; 'I' represents ideal MHD and 'H' represents pure hydrodynamics. The following letter is either 'n' (for an initial magnetic field in the negative z direction) or 'p' (for an initial magnetic field in the positive z direction). The next letter is 'h' (for 3e6 particles) or 'l' (for 3e5 particles). The extension P18 refers to the artificial resistivity algorithm from Price et al (2018), and TP13 refers to the artificial resistivity algorithm from Tricco & Price et al (2013). The numbers after this state the included dump files; the tarballs with 'misc' includes setup files, ascii output and other miscellaneous but relevant information. The data here is used for both this study and Wurster, Bate & Price (2018d): On the origin of fossil fields in stars. The data used for both publications are collapse17ph_P18_*, collapse16ph_P18_*, and collapseInh_P18_*. The data used in 2018c only are collapseHh_*, collapse17nh_P18_*, and collapse16nh_P18_*. The data used in 2018d only are collapse17ph_TP13_*, collapse17pl_P18_*, and collapseInl_P18_*. Related, but unpublished data are collapse17nh_TP13_*, and collapse17nl_P18_*.,The articles associated with this dataset are available in ORE at: http://hdl.handle.net/10871/33965 and http://hdl.handle.net/10871/34107,