The possibility that large flux differences between the poles and the equator at the bottom of the solar convective zone are compatible with the small differences observed at the surface is studied. The consequences of increasing the depth of the convective zone due to overshooting are explored. A Boussinesq model is used for the convective zone and it is assumed that the interaction of the global convection with rotation is modelled through a convective flux coefficient whose perturbed part is proportional to the local Taylor number. The numerical integration of the equations of motion and energy shows that coexistence between large pole-equator flux differences at the bottom and small ones at the surface is possible if the solar convective zone extends to a depth of 0.4 R(Sun). The angular velocity distribution inside the convective zone is in agreement with the ..cap alpha omega..-dynamo theories of the solar cycle.