  We explore a two-dimensional kinematic solar dynamo model in a full sphere,
based on the helioseismically determined solar rotation profile and with an
$\alpha$ effect concentrated near the solar surface, which captures the
Babcock--Leighton idea that the poloidal field is created from the decay of
tilted bipolar active regions. The meridional circulation, assumed to penetrate
slightly below the tachocline, plays an important role. Some doubts have
recently been raised regarding the ability of such a model to reproduce
solar-like dipolar parity. We specifically address the parity issue and show
that the dipolar mode is preferred when certain reasonable conditions are
satisfied, the most important condition being the requirement that the poloidal
field should diffuse efficiently to get coupled across the equator. Our model
is shown to reproduce various aspects of observational data, including the
phase relation between sunspots and the weak, diffuse field.
