  We present an analytic, quasi-local dynamo model for accretion discs threaded
by net, vertical magnetic flux. In a simple slab geometry and ignoring
stochastic mean-field dynamo effects, we calculate the large-scale field
resulting from the balance between kinematic field amplification and turbulent
resistive diffusion. The ability of the disc to accumulate magnetic flux is
sensitive to a single parameter dependent on the ratio of the vertical
resistive diffusion time to the Alfv\'en crossing time, and we show how the
saturation levels of magnetorotational and other instabilities can govern disc
structure and evolution. Under wide-ranging conditions, inflow is governed by
large-scale magnetic stresses rather than internal viscous stress. We present
models of such "magnetically boosted" discs and show that they lack a radiation
pressure-dominated zone. Our model can account for "magnetically elevated"
discs as well as instances of midplane outflow and field reversals with height
that have been seen in some global simulations. Using the time-dependent
features of our model, we find that the incorporation of dynamo effects into
disc structure can lead to steady or episodic "magnetically arrested discs"
(MADs) that maximize the concentration of magnetic flux in their central
regions.
