I will present new results of cosmological galaxy formation with
cosmic magnetic fields. The new simulations are quite unique because
of its usage of adaptive mesh refinement to cover a broad range of
spatial/time scale and its tests of cosmological primordial magnetic
fields. I will also introduce a new approach of stochastic models
to incorporate sub-grid physics of astrophysical magnetic fields in
cosmological galaxy formation simulation. Various applications of
the new simulation results will be briefly explained in the talk,
encouraging further usages of the results by the KASI people.