  In this paper we focus on the construction of stellar outflow models emerging
from a polar coronal hole-type region surrounded by a magnetosphere in the
equatorial regions during phases of quiescent accretion. The models are based
on initial analytical solutions. We adopt a meridionally self-similar solution
of the time-independent and axisymmetric MHD equations which describes
effectively a jet originating from the corona of a star. We modify
appropriately this solution in order to incorporate a physically consistent
stellar magnetosphere. We find that the closed fieldline region may exhibit
different behaviour depending on the associated boundary conditions and the
distribution of the heat flux. However, the stellar jet in all final
equilibrium states is very similar to the analytical one prescribed in the
initial conditions. When the initial net heat flux is maintained, the
magnetosphere takes the form of a dynamical helmet streamer with a quasi steady
state slow magnetospheric wind. With no heat flux, a small dead zone forms
around the equator, surrounded by a weak streamer, source of a low mass flux
magnetospheric ejection. An equilibrium with no streamer and a helmet shaped
dead zone is found when the coronal hole is larger and extends up to a reduced
closed fieldline static zone. The study demonstrates the robustness of
self-similar solutions and their ability to provide quasi-steady jet
simulations with realistic boundaries and surrounded by equatorial
magnetospheres.
