  We study the cosmic evolution of the magnetic fields of a large sample of
spiral galaxies in a cosmologically representative volume by employing a
semi-analytic galaxy formation model and numerical dynamo solver in tandem. We
start by deriving time- and radius-dependent galaxy properties using the
galform galaxy formation model, which are then fed into the nonlinear
mean-field dynamo equations. These are solved to give the large-scale (mean)
field as a function of time and galactocentric radius for a thin disc, assuming
axial symmetry. A simple prescription for the evolution of the small-scale
(random) magnetic field component is also adopted. We find that, while most
massive galaxies are predicted to have large-scale magnetic fields at redshift
z=0, a significant fraction of them are expected to contain negligible
large-scale field. Our model indicates that, for most of the galaxies
containing large-scale magnetic fields today, the mean-field dynamo becomes
active at z<3. We compute the radial profiles of pitch angle, and find broad
agreement with observational data for nearby galaxies.
