Context :

Aims : We present the results of global 3-D MHD simulations of stratified and turbulent protoplanetary disc models .
The aim of this work is to develop thin disc models capable of sustaining turbulence for long run times , which can be used for on–going studies of planet formation in turbulent discs .

Methods : The results are obtained using two codes written in spherical coordinates : GLOBAL and NIRVANA .
Both are time–explicit and use finite differences along with the Constrained Transport algorithm to evolve the equations of MHD .

Results : In the presence of a weak toroidal magnetic field , a thin protoplanetary disc in hydrostatic equilibrium is destabilised by the magnetorotational instability ( MRI ) .
When the resolution is large enough ( \sim 25 vertical grid cells per scale height ) , the entire disc settles into a turbulent quasi steady–state after about 300 orbits .
Angular momentum is transported outward such that the standard \alpha parameter is roughly 4 - 6 \times 10 ^ { -3 } .
We find that the initial toroidal flux is expelled from the disc midplane and that the disc behaves essentially as a quasi–zero net flux disc for the remainder of the simulation .
As in previous studies , the disc develops a dual structure composed of an MRI–driven turbulent core around its midplane , and a magnetised corona stable to the MRI near its surface .
By varying disc parameters and boundary conditions , we show that these basic properties of the models are robust .

Conclusions : The high resolution disc models we present in this paper achieve a quasi–steady state and sustain turbulence for hundreds of orbits .
As such , they are ideally suited to the study of outstanding problems in planet formation such as disc–planet interactions and dust dynamics .