  Outflows from quasars inevitably pollute the intergalactic medium (IGM) with
magnetic fields. The short-lived activity of a quasar leaves behind an
expanding magnetized bubble in the IGM. We model the expansion of the remnant
quasar bubbles and calculate their distribution as a function magnetic field
strength at different redshifts. We find that by a redshift z ~ 3, about 5-80%
of the IGM volume is filled by magnetic fields with an energy density > 10% of
the mean thermal energy density of a photo-ionized IGM (at ~ 10^4 K). As
massive galaxies and X-ray clusters condense out of the magnetized IGM, the
adiabatic compression of the magnetic field could result in the fields observed
in these systems without a need for further dynamo amplification.
