The transport of angular momentum is one of the most important outstanding problems in astrophysical accretion disk physics. High angular momentum material forms a disk around the accreting object, which can be a forming protostar, a binary companion star, a stellar mass black hole, or even a supermassive black hole. In each of these cases, the magnetorotational instability (MRI) is believed to play a (possibly dominant) role in transporting angular momentum outward, allowing the disk material to fall onto the central object. Previous work has established that the MRI can drive turbulence which in turn can generate by dynamo action the requisite magnetic fields. We report on a series of numerical experiments aimed at understanding the operation of this MRI dynamo over a range of parameters, which while far from realistic, allow some insight into the scaling of the dynamo action.