  The origin of intergalactic magnetic fields is still a mystery and several
scenarios have been proposed so far: among them, primordial phase transitions,
structure formation shocks and galactic outflows. In this work we investigate
how efficiently galactic winds can provide an intense and widespread "seed"
magnetisation. This may be used to explain the magnetic fields observed today
in clusters of galaxies and in the intergalactic medium (IGM). We use
semi-analytic simulations of magnetised galactic winds coupled to high
resolution N-body simulations of structure formation to estimate lower and
upper limits for the fraction of the IGM which can be magnetised up to a
specified level. We find that galactic winds are able to seed a substantial
fraction of the cosmic volume with magnetic fields. Most regions affected by
winds have magnetic fields in the range -12 < Log B < -8 G, while higher seed
fields can be obtained only rarely and in close proximity to wind-blowing
galaxies. These seed fields are sufficiently intense for a moderately efficient
turbulent dynamo to amplify them to the observed values. The volume filling
factor of the magnetised regions strongly depends on the efficiency of winds to
load mass from the ambient medium. However, winds never completely fill the
whole Universe and pristine gas can be found in cosmic voids and regions
unaffected by feedback even at z=0. This means that, in principle, there might
be the possibility to probe the existence of primordial magnetic fields in such
regions.
