  In parts I and II, we determined which faithful irreducible representations
$V$ of a simple linear algebraic group $G$ are generically free for Lie($G$),
i.e., which $V$ have an open subset consisting of vectors whose stabilizer in
Lie($G$) is zero, with some assumptions on the characteristic of the field.
This paper settles the remaining cases, which are of a different nature because
Lie($G$) has a more complicated structure and there need not exist general
dimension bounds of the sort that exist in good characteristic.
