The compelling observational evidence for strongly magnetized accretion disks around black holes and their attractive theoretical properties warrant an investigation into how such a disk magnetization state can develop and persist. The structure and evolution of these disks are governed by a dynamo-like mechanism, which channels part of the accretion power liberated by the magnetorotational instability (MRI) into an ordered toroidal magnetic field. To study this dynamo activity, we performed a suite of accretion disk simulations in the local limit ( i.e., shearing boxes). We find that the entire disk develops into a magnetic pressure-dominated state for a sufficiently strong net vertical magnetic flux and dynamo activity persists. Still stronger fields result in a highly inhomogeneous disk structure, with large density fluctuations. Finally, we show that the magnetized state of the disk in our simulations is well-matched by an analytic model describing the creation and buoyant escape of toroidal field.