We present shell dynamo models for the solar convection zone with positive alpha -effect in the northern hemisphere and a meridional circulation which is directed equatorward at the bottom and poleward at the top of the convection zone. Two different rotation patterns are used: a simple variation of the rotation rate with depth and the rotation law as derived by helioseismology. Depending on the Reynolds number associated with the meridional flow, the dynamo shows a whole ``zoo'' of solutions. For sufficiently small values of the eddy magnetic diffusivity (1011 cm2/s), field advection by the meridional flow becomes dominant and even changes the character of the butterfly diagram. Flow amplitudes of a few m/s are then sufficient to turn the originally ``wrong'' butterfly diagram into a ``solar-type'' butterfly diagram, i.e. with activity belts drifting equatorward. This effect can easily be demonstrated with a super-rotation law (partial \Omegaega /partial r > 0) with $Omega ega$ independent of the latitude. The situation is much more complicated for the ``real'' rotation law with the observed strong negative shear at high latitudes. With zero meridional flow, oscillating solutions are found without any latitudinal migration of the toroidal field belts, neither poleward nor equatorward. Small but finite flow amplitudes cause the magnetic field belts to drift poleward while in case of fast flow they move equatorward.