  We study multicolour, oriented and high-dimensional discrepancies of the set
of all subtrees of a tree. As our main result, we show that the $r$-colour
discrepancy of the subtrees of any tree is a linear function of the number of
leaves $\ell$ of that tree. More concretely, we show that it is bounded by
$\lceil(r-1)\ell/r\rceil$ from below and $\lceil(r-1)\ell/2\rceil$ from above,
and that these bounds are asymptotically sharp. Motivated by this result, we
introduce natural notions of oriented and high-dimensional discrepancies and
prove bounds for the corresponding discrepancies of the set of all subtrees of
a given tree as functions of its number of leaves.
