Counting points of fixed degree and given height over function fields

Let $k$ be a finite field extension of the function field ${\text{bfF}}_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$withgivenheightandoffixeddegree$d$overthefield$k$. If $n>2d+3$ we derive an asymptotic estimate for their number as the height tends to infinity. As an application we also deduce asymptotic estimates for certain decomposable forms.