  The Sun and other cool stars harbouring outer convection zones manifest
magnetic activity in their atmospheres. The connection between this activity
and the properties of a deep-seated dynamo generating the magnetic flux is not
well understood. By employing physical models, we study the spatial and
temporal characteristics of the observable surface field for various stellar
parameters. We combine models for magnetic flux generation, buoyancy
instability, and transport, which encompass the entire convection zone. The
model components are: (1) a thin-layer alpha-Omega dynamo at the base of the
convection zone; (2) buoyancy instabilities and the rise of flux tubes through
the convection zone in 3D, which provides a physically consistent determination
of emergence latitudes and tilt angles; and (3) horizontal flux transport at
the surface. For solar-type stars and rotation periods longer than about 10
days, the latitudinal dynamo waves generated by the deep-seated alpha-Omega
dynamo are faithfully reflected by the surface distribution of magnetic flux.
For rotation periods of the order of two days, however, Coriolis acceleration
of rising flux loops leads to surface flux emergence at much higher latitudes
than the dynamo waves at the bottom of the convection zone reach. A similar
result is found for a K0V star with a rotation period of two days. In the case
of a rapidly rotating K1 subgiant, overlapping dynamo waves lead to noisy
activity cycles and mixed-polarity fields at high latitudes.
