  We continue a line of research which studies which hereditary families of
digraphs have bounded dichromatic number. For a class of digraphs
$\mathcal{C}$, a hero in $\mathcal{C}$ is any digraph $H$ such that $H$-free
digraphs in $\mathcal{C}$ have bounded dichromatic number. We show that if $F$
is an oriented star of degree at least five, the only heroes for the class of
$F$-free digraphs are transitive tournaments. For oriented stars $F$ of degree
exactly four, we show the only heroes in $F$-free digraphs are transitive
tournaments, or possibly special joins of transitive tournaments. Aboulker et
al. characterized the set of heroes of $\{H, K_{1} + \vec{P_{2}}\}$-free
digraphs almost completely, and we show the same characterization for the class
of $\{H, rK_{1} + \vec{P_{3}}\}$-free digraphs. Lastly, we show that if we
forbid two "valid" orientations of brooms, then every transitive tournament is
a hero for this class of digraphs.
