  The concentration of magnetic flux near the poles of rapidly rotating cool
stars has been recently proposed as an alternative mechanism to dynamo
saturation in order to explain the saturation of angular momentum loss. In this
work we study the effect of magnetic surface flux distribution on the coronal
field topology and angular momentum loss rate. We investigate if magnetic flux
concentration towards the pole is a reasonable alternative to dynamo
saturation. We construct a 1D wind model and also apply a 2-D self-similar
analytical model, to evaluate how the surface field distribution affects the
angular momentum loss of the rotating star. From the 1D model we find that, in
a magnetically dominated low corona, the concentrated polar surface field
rapidly expands to regions of low magnetic pressure resulting in a coronal
field with small latitudinal variation. We also find that the angular momentum
loss rate due to a uniform field or a concentrated field with equal total
magnetic flux is very similar. From the 2D wind model we show that there are
several relevant factors to take into account when studying the angular
momentum loss from a star. In particular, we show that the inclusion of force
balance across the field in a wind model is fundamental if realistic
conclusions are to be drawn from the effect of non-uniform surface field
distribution on magnetic braking. This model predicts that a magnetic field
concentrated at high latitudes leads to larger Alfven radii and larger braking
rates than a smoother field distribution. From the results obtained, we argue
that the magnetic surface field distribution towards the pole does not directly
limit the braking efficiency of the wind.
