Not yet reviewed by Pith; the record is open.

The convective envelopes of cool main-sequence stars harbour magnetic fields with a complex global and local structure. These fields affect the near-surface convection and the outer stellar atmospheres in many ways and are responsible for the observable magnetic activity of stars. Our aim is to understand the local structure in unipolar regions with moderate average magnetic flux density. These correspond to plage regions covering a substantial fraction of the surface of the Sun (and likely also the surface of other Sun-like stars) during periods of high magnetic activity. We analyse the results of 18 local-box magnetohydrodynamics simulations covering the upper layers of the convection zones and the photospheres of cool main-sequence stars of spectral types F to early M. The average vertical field in these simulations ranges from 20 to 500G. We find a substantial variation of the properties of the surface magnetoconvection between main-sequence stars of different spectral types. As a consequence of a reduced efficiency of the convective collapse of flux tubes, M dwarfs lack bright magnetic structures in unipolar regions of moderate field strength. The spatial correlation between velocity and the magnetic field as well as the lifetime of magnetic structures and their sizes relative to the granules vary significantly along the model sequence of stellar types.