  We seek to characterize how the change of global rotation rate influences the
overall dynamics and large scale flows arising in the convective envelopes of
stars covering stellar spectral types from early G to late K. We do so through
numerical simulations with the ASH code, where we consider stellar convective
envelopes coupled to a radiative interior with various global properties. As
solar-like stars spin down over the course of their main sequence evolution,
such change must have a direct impact on their dynamics and rotation state. We
indeed find that three main states of rotation may exist for a given star:
anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow
poles), or a cylindrical rotation profile. Under increasingly strict rotational
constraints, the latter profile can further evolve into a Jupiter-like profile,
with alternating prograde and retrograde zonal jets. We have further assessed
how far the convection and meridional flows overshoot into the radiative zone
and investigated the morphology of the established tachocline. Using simple
mixing length arguments, we are able to construct a scaling of the fluid Rossby
number $R_{of} = \tilde{\omega}/2\Omega_* \sim \tilde{v}/2\Omega_* R_*$, which
we calibrate based on our 3-D ASH simulations. We can use this scaling to map
the behavior of differential rotation versus the global parameters of stellar
mass and rotation rate. Finally, we isolate a region on this map ($R_{of}
\gtrsim 1.5-2$) where we posit that stars with an anti-solar differential
rotation may exist in order to encourage observers to hunt for such targets.
