  The atmospheres of cool main-sequence stars are structured by convective
flows from the convective envelope that penetrate the optically thin layers and
lead to structuring of the stellar atmospheres analogous to solar granulation.
The flows have considerable influence on the 3D structure of temperature and
pressure and affect the profiles of spectral lines formed in the photosphere.
For the set of six 3D radiative (M)HD simulations of cool main-sequence stars
described in the first paper of this series, we analyse the near-surface
layers. We aim at describing the properties of granulation of different stars
and at quantifying the effects on spectral lines of the thermodynamic structure
and flows of 3D convective atmospheres. We detected and tracked granules in
brightness images from the simulations to analyse their statistical properties,
as well as their evolution and lifetime. We calculated spatially resolved
spectral line profiles using the line synthesis code SPINOR. To enable a
comparison to stellar observations, we implemented a numerical
disc-integration, which includes (differential) rotation. Although the stellar
parameters change considerably along the model sequence, the properties of the
granules are very similar. The impact of the 3D structure of the atmospheres on
line profiles is measurable in disc-integrated spectra. Line asymmetries caused
by convection are modulated by stellar rotation. The 3D structure of cool
stellar atmospheres as shaped by convective flows has to be taken into account
when using photospheric lines to determine stellar parameters.
