We resolve the paradox that although magnetic collimation of an isotropic s
olar wind results in an enhancement of its proton flux along the polar dire
ctions, several observations indicate a wind proton flux peaked at the equa
tor. To that goal, we solve the full set of the time-dependent MHD equation
s describing the axisymmetric outflow of plasma from the magnetized and rot
ating 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 colli
mation properties of the solar outflow at large heliocentric distances. For
the present day solar wind it is found that the poloidal streamlines and f
ieldlines are only slightly focused toward the solar poles. However, even s
uch 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) observati
ons. For the anisotropic in heliolatitude wind with parameters at the base
inferred from in situ observations by ULYSSES/SWOOPS and SOHO/CDS the effec
t 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 ea
rlier phase of our Sun. For such conditions it is found that for initially
radial streamlines, the azimuthal magnetic field created by the fast rotati
on focus them toward the rotation axis and forms a tightly collimated jet.