We have already mentioned that outflows from supernovae and AGN could seed galaxies and clusters with magnetic fields. We now consider whether such processes could in fact magnetize the general intergalactic medium and if so at what levels.
In this context it is interesting to note that there is growing evidence for metals in the moderately overdense intergalactic medium (IGM) up to redshifts z ~ 5 or so (cf.  and references therein). The metals detected in the IGM can only have been synthesized by stars in galaxies, and galactic outflows energized by supernovae (SNe) are the primary means by which they can be transported from galaxies into the IGM. If galactic ISM is also magnetized due to some form of dynamo action, then such outflows will also transport magnetic fields into the IGM. One can roughly estimate the IGM field resulting from such outflows, by using magnetic flux conservation under spherically symmetric expansion; that is Bseed (IGM / ISM)2/3 Bgal. For Bgal 3 µG, and IGM / ISM 10-6, one gets Bseed 0.3 nG. In a similar fashion outflows from AGN can also transport magnetized plasma into the IGM.
The level of such magnetization cannot be estimated at present with any great certainty, since it depends not only on a host of parameters to do with the energetics of the outflows but also on the evolution of the magnetic field in the outflow, whether it is amplified by dynamo action or decays by generating decaying MHD turbulence. Nevertheless there are several attempts  where some model of the outflows is tied in with a model of magnetic field behaviour. For example Bertone et al (in ) find the outflows affected regions can have fields ranging from 10-12 - 10-8 G, not much of a volume filling at z = 3 but a significant volume filling by z = 0. Due to outflows from AGN, Furlanetto and Loeb (in ) estimate that by a redshift z ~ 3, about 5%-20% of the IGM volume is filled by magnetic fields and the magnetic pressure in these regions could be comparable to the thermal pressure of the the photoionized IGM (at T ~ 104 K).
It should also be noted that such outflow scenarios are constrained by the fact that they should not dynamically perturb the IGM responsible for the Lyman- forest absorption at z=3. In this context scenarios involving outflows from small mass galaxies and filling the IGM at high redshifts are more favored, for magnetizing the high z IGM significantly , without perturbing the Lyman- forest.
Of course, as mentioned earlier, one still needs to mix the magnetized and unmagnetized media and what this does to both the field strength and coherence scale is as yet unclear. This would be relevant if we wish to use the IGM field to explain galaxy and cluster magnetism. Nevertheless,the magnetization of a significant volume of the IGM by z = 0 could impact significantly on other astrophysical phenomena. For example significant IGM magnetic fields would perturb cosmic ray propagation and is relevant to the issue of whether one can do high-energy cosmic ray astronomy at all.