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 .