  We resolve the paradox that although magnetic collimation of an isotropic
solar wind results in an enhancement of its proton flux along the polar
directions, several observations indicate a wind proton flux peaked at the
equator. To that goal, we solve the full set of the time-dependent MHD
equations describing the axisymmetric outflow of plasma from the magnetized and
rotating Sun, either in its present form of the solar wind, or, in its earlier
form of a protosolar wind. Special attention is directed towards the
collimation properties of the solar outflow at large heliocentric distances.
For the present day solar wind it is found that the poloidal streamlines and
fieldlines are only slightly focused toward the solar poles. However, even such
a modest compression of the flow by the azimuthal magnetic field would lead to
an increase of the mass flux at the polar axis by about 20% at 1 AU, relatively
to its value at the equator, for an initially isotropic at the base wind,
contrary to older and recent (Prognoz, Ulysses, SOHO) observations. For the
anisotropic in heliolatitude wind with parameters at the base inferred from in
situ observations by ULYSSES/SWOOPS and SOHO/CDS the effect of collimation is
almost totally compensated by the initial velocity and density anisotropy of
the wind. This effect should be taken into account in the interpretation of the
recent SOHO observations by the SWAN instrument. Similar simulations have been
performed for a five- and ten-fold increase of the solar angular velocity
corresponding presumably to the wind of an earlier phase of our Sun. For such
conditions it is found that for initially radial streamlines, the azimuthal
magnetic field created by the fast rotation focus them toward the rotation axis
and forms a tightly collimated jet.
