  (abridged) Context: The mechanisms that cause the formation of sunspots are
still unclear. Aims: We study the self-organisation of initially uniform
sub-equipartition magnetic fields by highly stratified turbulent convection.
Methods: We perform simulations of magnetoconvection in Cartesian domains that
are $8.5$-$24$ Mm deep and $34$-$96$ Mm wide. We impose either a vertical or a
horizontal uniform magnetic field in a convection-driven turbulent flow.
Results: We find that super-equipartition magnetic flux concentrations are
formed near the surface with domain depths of $12.5$ and $24$ Mm. The size of
the concentrations increases as the box size increases and the largest
structures ($20$ Mm horizontally) are obtained in the 24 Mm deep models. The
field strength in the concentrations is in the range of $3$-$5$ kG. The
concentrations grow approximately linearly in time. The effective magnetic
pressure measured in the simulations is positive near the surface and negative
in the bulk of the convection zone. Its derivative with respect to the mean
magnetic field, however, is positive in the majority of the domain, which is
unfavourable for the negative effective magnetic pressure instability (NEMPI).
Furthermore, we find that magnetic flux is concentrated in regions of
converging flow corresponding to large-scale supergranulation convection
pattern. Conclusions: The linear growth of large-scale flux concentrations
implies that their dominant formation process is tangling of the large-scale
field rather than an instability. One plausible mechanism explaining both the
linear growth and the concentrate on of the flux in the regions of converging
flow pattern is flux expulsion. Possible reasons for the absence of NEMPI are
that the derivative of the effective magnetic pressure with respect to the mean
magnetic field has an unfavourable sign and that there may not be sufficient
scale separation.
