  In order to study the structure of arbitrary split Leibniz triple systems, we
introduce the class of split Leibniz triple systems as the natural extension of
the class of split Lie triple systems and split Leibniz algebras. By developing
techniques of connections of roots for this kind of triple systems, we show
that any of such Leibniz triple systems $T$ with a symmetric root system is of
the form $T=U+\sum_{[j]\in \Lambda^{1}/\sim} I_{[j]}$ with $U$ a subspace of
$T_{0}$ and any $I_{[j]}$ a well described ideal of $T$, satisfying
$\{I_{[j]},T,I_{[k]}\} =\{I_{[j]},I_{[k]},T\}=\{T,I_{[j]},I_{[k]}\}=0$ if
$[j]\neq [k]$.
