  Observations of active stars reveal highly non-uniform surface distributions
of magnetic flux. Theoretical models considering magnetised stellar winds
however often presume uniform surface magnetic fields, characterised by a
single magnetic field strength. The present work investigates the impact of
non-uniform surface magnetic field distributions on the stellar mass and
angular momentum loss rates. The approach of Weber & Davis (1967) is extended
to non-equatorial latitudes to quantify the impact of latitude-dependent
magnetic field distributions over a large range of stellar rotation rates and
thermal wind properties. The analytically prescribed field patterns are
dominated by magnetic flux concentrations at intermediate and high latitudes.
The global stellar mass loss rates are found to be rather insensitive to
non-uniformities of the surface magnetic field. Depending on the non-uniformity
of the field distribution, the angular momentum loss rates deviate in contrast
at all rotation rates between -60% and 10% from the Weber & Davis-values, and
the effective Alfvenic radii up to about +/-25%. These large variations albeit
equal amounts of total magnetic flux indicate that a classification of stellar
surface magnetic fields through a single field strength is insufficient, and
that their non-uniformity has to be taken into account. The consequences for
applications involving magnetised stellar winds are discussed in view of the
rotational evolution of solar-like stars and of the observational determination
of their mass loss rates using the terminal velocity and ram pressure of the
wind. For rapidly rotating stars the latitudinal variation of the wind ram
pressure is found to exceed, depending on the actual field distribution on the
stellar surface, over two orders of magnitude.
