I am looking for an article or book where the theory of heights over function fields (in any characteristic) is treated. I am especially interested in Northcott-type statements. For instance, over a function field $K$ over $\bf Q$, say, a subvariety $X$ of ${\bf P}^n_{K}$, which has a dense subset of $K$-points with bounded height, should have a model over (possibly a finite extension of) $\bf Q$. Where can I find the proof of such a statement ? When $K$ is a function field over a finite field, then one can use Hilbert schemes to get Northcott-type finiteness statements but in general, it seems that one should combine the theory of Hilbert schemes with some descent arguments. I would be grateful for any suggestions.