  A sibling of a relational structure $R$ is any structure $S$ which can be
embedded into $R$ and, vice versa, in which $R$ can be embedded. Let $sib(R)$
be the number of siblings of $R$, these siblings being counted up to
isomorphism. Thomass\'e conjectured that for countable relational structures
made of at most countably many relations, $sib(R)$ is either $1$, countably
infinite, or the size of the continuum; but even showing the special case
$sib(R)=1$ or infinite is unsettled when $R$ is a countable tree. This is
related to Bonato-Tardif conjecture asserting that for every tree $T$ the
number of trees which are sibling of $T$ is either one or infinite.
  We prove that if $R$ is countable and $\aleph_{0}$-categorical, then indeed
$sib(R)$ is one or infinite. Furthermore, $sib(R)$ is one if and only if $R$ is
finitely partitionable in the sense of Hodkinson and Macpherson. The key tools
in our proof are the notion of monomorphic decomposition of a relational
structure introduced in a paper by Pouzet and Thi\'ery 2013 and studied further
by Oudrar and Pouzet 2015, and a result of Frasnay 1984.
