  We present a series of radiative MHD simulations addressing the origin and
distribution of mixed polarity magnetic field in the solar photosphere. To this
end we consider numerical simulations that cover the uppermost 2-6 Mm of the
solar convection zone and we explore scales ranging from 2 km to 25 Mm. We
study how the strength and distribution of magnetic field in the photosphere
and subsurface layers depend on resolution, domain size and boundary
conditions. We find that 50% of the magnetic energy at the \tau=1 level comes
from field with the less than 500 G strength and that 50% of the energy resides
on scales smaller than about 100 km. While probability distribution functions
are essentially independent of resolution, properly describing the spectral
energy distribution requires grid spacings of 8 km or smaller. The formation of
flux concentrations in the photosphere exceeding 1 kG requires a mean vertical
field strength greater than 30-40 G at \tau=1. The filling factor of kG flux
concentrations increases with overall domain size as magnetic field becomes
organized by larger, longer lived flow structures. A solution with a mean
vertical field strength of around 85 G at \tau=1 requires a subsurface RMS
field strength increasing with depth at the same rate as the equipartition
field strength. We consider this an upper limit for the quiet Sun field
strength, which implies that most of the convection zone is magnetized close to
equipartition. We discuss these findings in view of recent high-resolution
spectropolarimetric observations of quiet Sun magnetism.
