  We make the elementary observation that the Lagrangian submanifolds of
$\mathbb{C}^n$, for each $n \ge 3$, constructed by Ekholm, Eliashberg, Murphy
and Smith are non-uniruled and moreover have infinite relative Gromov width.
The construction of these submanifolds use exact Lagrangian caps, which
obviously are non-uniruled in themselves. This property is also used to show
that if a Legendrian submanifold inside a 1-jet space admits an exact
Lagrangian cap then its Legendrian contact homology DGA is acyclic.
