  We have carried out and analyzed a set of axisymmetric MHD simulations of the
evolution of a turbulent/diffusive accretion disc around an initially
unmagnetized star. The disc is initially threaded by a weak magnetic field
where the magnetic pressure is significantly less than the kinetic pressure in
the disc. The viscosity and magnetic diffusivity are modelled by two "alpha"
parameters, while the coronal region above the disc is treated using ideal MHD.
The initial magnetic field is taken to consist of three poloidal field loops
threading the disc. The motivation for this study is to understand the
advection of disc matter and magnetic field by the turbulent/diffusive disc. At
early times the innermost field loop twists and its field lines become open.
The twisting of the opened field lines leads to the formation of both an inner
collimated, magnetically-dominated jet, and at larger distances from the axis a
matter dominated uncollimated wind. For later times, the strength of the
magnetic field decreases owing to field reconnection and annihilation in the
disc. For the early times, we have derived from the simulations both the matter
accretion speed in the disc and the accretion speed of the magnetic field. We
show that the derived matter accretion speed agrees approximately with the
predictions of a model where the accretion speed is the sum of two terms, one
due to the disc's viscosity (which gives a radial outflow of angular momentum
in the disc), and a second due to the twisted magnetic field at the disc's
surface (which gives a vertical outflow of angular momentum). For early times
we find that the magnetic contribution is roughly twice the viscous
contribution for the case where the alpha parameters are both equal to 0.1. At
later times the magnetic contribution to the matter speed becomes small
compared to the viscous contribution.
