  Given partitions $\alpha$, $\beta$, $\gamma$, the short exact sequences $0\to
N_\alpha \to N_\beta \to N_\gamma \to 0$ of nilpotent linear operators of
Jordan types $\alpha$, $\beta$, $\gamma$, respectively, define a constructible
subset $\mathbb V_{\alpha,\gamma}^\beta$ of an affine variety. Geometrically,
the varieties $\mathbb V_{\alpha,\gamma}^\beta$ are of particular interest as
they occur naturally and since they typically consist of several irreducible
components. In fact, each Littlewood-Richardson (LR-) tableau $\Gamma$ of shape
$(\alpha,\beta,\gamma)$ contributes one irreducible component
$\overline{\mathbb V}_\Gamma$.
  We consider the partial order $\Gamma\leq_{\sf bound}^*\widetilde{\Gamma}$ on
LR-tableaux which is the transitive closure of the relation given by $\mathbb
V_{\widetilde{\Gamma}}\cap \overline{\mathbb V}_\Gamma\neq \emptyset$. In this
paper we compare the boundary relation with partial orders given by algebraic,
combinatorial and geometric conditions. It is known that in the case where the
parts of $\alpha$ are at most two, all those partial orders are equivalent. We
prove that those partial orders are also equivalent in the case where
$\beta\setminus\gamma$ is a horizontal and vertical strip. Moreover, we discuss
how the orders differ in general.
