  Seaweed Lie algebras are a natural generalisation of parabolic subalgebras of
reductive Lie algebras. The well-known Richardson Theorem says that the adjoint
action of a parabolic group has a dense open orbit in the nilpotent radical of
its Lie algebra \cite{richardson}. We call elements in the open orbit
Richardson elements. In \cite{JSY} together with Yu, we generalized
Richardson's Theorem and showed that Richardson elements exist for seaweed Lie
algebras of type $\mathbb{A}$. Using GAP, we checked that Richardson elements
exist for all exceptional simple Lie algebras except $\mathbb{E}_8$, where we
found a counterexample.
  In this paper, we complete the story on Richardson elements for seaweeds of
finite type, by showing that they exist for any seaweed Lie algebra of type
$\mathbb{B}$, $\mathbb{C}$ and $\mathbb{D}$. By decomposing a seaweed into a
sum of subalgebras and analysing their stabilisers, we obtain a sufficient
condition for the existence of Richarson elements. The sufficient condition is
then verified using quiver representation theory. More precisely, using the
categorical construction of Richardson elements in type $\mathbb{A}$, we prove
that the sufficient condition is satisfied for all seaweeds of type
$\mathbb{B}$, $\mathbb{C}$ and $\mathbb{D}$, except in two special cases, where
we give a directproof.
