  [Abridged abstract:] Stellar activity data provide evidence of activity wave
branches propagating polewards rather than equatorwards (the solar case).
Stellar dynamo theory allows polewards propagating dynamo waves for certain
governing parameters. We try to unite observations and theory, restricting our
investigation to the simplest mean-field dynamo models. We suggest a crude
preliminary systematization of the reported cases of polar activity branches.
Then we present results of dynamo model simulations which contain magnetic
structures with polar dynamo waves, and identify the models which look most
promising for explaining the latitudinal distribution of spots in dwarf stars.
Those models require specific features of stellar rotation laws, and so
observations of polar activity branches may constrain internal stellar
rotation. Specifically, we find it unlikely that a pronounced poleward branch
can be associated with a solar-like internal rotation profile, while it can be
more readily reproduced in the case of a cylindrical rotation law appropriate
for fast rotators. We stress the case of the subgiant component of the active
close binary HR 1099 which, being best investigated, presents the most severe
problems for a dynamo interpretation. Our best model requires dynamo action in
two layers separated in radius. Observations of polar activity branches provide
valuable information for understanding stellar activity mechanisms and internal
rotation, and thus deserve intensive observational and theoretical
investigation. Current stellar dynamo theory seems sufficiently robust to
accommodate the phenomenology.
