  Stellar magnetic activity of solar like stars is thought to be due to an
internal dynamo. While the Sun has been the subject of intense research for
refining dynamo models, observations of magnetic cyclic activity in solar type
stars have become more and more available, opening a new path to understand the
underlying physics behind stellar cycles. For instance, it is key to understand
how stellar rotation rate influences magnetic cycle period $\Pcyc$. Recent
numerical simulations of advection-dominated Babcock Leighton models have
demonstrated that it is difficult to explain this observed trend given a) the
strong influence of the cycle period to the meridional circulation amplitude
and b) the fact that 3D models indicate that meridional flows become weaker as
the rotation rate increases. In this paper, we introduce the turbulent pumping
mechanism as another advective process capable also of transporting the
magnetic fields. We found that this model is now able to reproduce the
observations under the assumption that this effect increases as $\Omega^2$. The
turbulent pumping becomes indeed another major player able to circumvent the
meridional circulation. However, for high rotation rates ($\Omega \simeq 5
\Omega_\odot$), its effects dominate those of the meridional circulation,
entering a new class of regime dominated by the advection of turbulent pumping
and thus leading to a cyclic activity qualitatively different from that of the
sun.
