  A linkage in a graph $G$ of size $k$ is a subgraph $L$ of $G$ whose connected
components are $k$ paths. The pattern of a linkage of size $k$ is the set of
$k$ pairs formed by the endpoints of these paths. A consequence of the Unique
Linkage Theorem is the following: there exists a function
$f:\mathbb{N}\to\mathbb{N}$ such that if a plane graph $G$ contains a sequence
$\mathcal{C}$ of at least $f(k)$ nested cycles and a linkage of size at most
$k$ whose pattern vertices lay outside the outer cycle of $\mathcal{C},$ then
$G$ contains a linkage with the same pattern avoiding the inner cycle of
$\mathcal{C}$. In this paper we prove the following variant of this result:
Assume that all the cycles in $\mathcal{C}$ are "orthogonally" traversed by a
linkage $P$ and $L$ is a linkage whose pattern vertices may lay either outside
the outer cycle or inside the inner cycle of
$\mathcal{C}:=[C_{1},\ldots,C_{p},\ldots,C_{2p-1}]$. We prove that there are
two functions $g,f:\mathbb{N}\to\mathbb{N}$, such that if $L$ has size at most
$k$, $P$ has size at least $f(k),$ and $|\mathcal{C}|\geq g(k)$, then there is
a linkage with the same pattern as $L$ that is "internally combed" by $P$, in
the sense that $L\cap C_{p}\subseteq P\cap C_{p}$. In fact, we prove this
result in the most general version where the linkage $L$ is $s$-scattered: no
two vertices of distinct paths of $L$ are within distance at most $s$. We
deduce several variants of this result in the cases where $s=0$ and $s>0$.
These variants permit the application of the unique linkage theorem on several
path routing problems on embedded graphs.
