Understanding angular momentum transport in accretion discs is fundamental to explaining the formation of systems on all scales, from satellite systems, to planetary systems. Turbulence, driven by the magneto-rotational instability (MRI), transports angular momentum outwards allowing accretion on to the central object. However, the MRI may be suppressed by a low ionisation fraction and dead zones can form at the disc midplane. Dead zones are regions with no turbulence that prevent the free flow of material through the disc. Material accumulates in the dead zone and the disc becomes gravo-magneto unstable. Accretion on to the central object occurs in outbursts involving a large fraction of the disc mass. We explain the outbursts as transitions between steady state solutions, one that is fully turbulent and a second that is self-gravitating. Outbursts have been observed in young stellar objects such as FU Orionis systems and we find they should also occur in circumplanetary discs around planets forming from a circumstellar disc. The increased luminosity of the circumplanetary disc during the outbursts may aid planet detection during the early stages of planet formation.