We have investigated the properties of gravito-turbulent discs in 3D using high-resolution shearing-box simulations. For large enough domain sizes, $Ly\gtrsim 60H$, the disc settles down into a quasi-steady state, showing no long term trends in properties or variation with box size. For smaller boxes, we find that the azimuthal wavelength of the dominant spiral modes are limited to the domain size. This is associated with a bursty behaviour that differs from the quasi-steady dynamics at larger sizes. We point out that a similar transition may be expected in global simulations at the point where the range of azimuthal wavelengths is limited by the finite disc size. This condition (i.e. when $60H\sim 2\pi R$, i.e. $H/R\sim 0.1$) correctly predicts the transition to bursty behaviour previously found in global simulations for disc-to-star mass ratios in excess of 0.25. We recover a transition in the dynamics from two- to three-dimensional behaviour, characterized by a turbulence that becomes more isotropic on small scales. This turbulence likely plays an important role in the evolution of dust in self-gravitating discs, potentially dominating the collision velocity for particles with Stokes number . Finally, we consider the stability of gravito-turbulence against fragmentation, finding that discs which cool faster than a few dynamical times fragment immediately, supporting previous results. We also find hints of stochastic fragmentation at marginally longer cooling times, in which a fragment forms from a quasi-equilibrium state. However, this makes little practical difference to region where planet formation via gravitational instability may occur.