This paper introduces a new class of analytic MHD solutions for steady
, axisymmetric, rotating outflows interacting with poleward deflected,
partially open magnetic fields. In the first paper of this series, se
veral simplifying assumptions were necessary to deal with the problem
in an analytical fashion, One of the most important restrictive hypoth
eses is the spherical symmetry of the Mach-Alfven surfaces. This condi
tion is relaxed in this work, and general colatitude-dependent Alfveni
c surfaces are assumed. As an example of the method, approximate solut
ions are found for a purely radial magnetic configuration and for init
ially superalfvenic outflows, by assuming a small-amplitude anisotropi
c component of the Mach-Alfven function regarding the spherically symm
etric part. It is shown that the general behavior of the stellar wind
drastically changes. Particularly, for the sample of solutions derived
here it is found that the terminal velocity of the wind does not dive
rge and increases with rotation. The energy distribution needed to sus
tain the outflow consists of a heating source located close to the pho
tosphere, and its rate is much smaller than the blackbody power radiat
ed by the star. The temperature profile displays the typical chromosph
eric structure of early-type stars once its associated set of boundary
conditions is given.