  We study the structure of a Leibniz triple system $\mathcal{E}$ graded by an
arbitrary abelian group $G$ which is considered of arbitrary dimension and over
an arbitrary base field $\mathbb{K}$. We show that $\mathcal{E}$ is of the form
$\mathcal{E}=U+\sum_{[j]\in \sum^{1}/\sim} I_{[j]}$ with $U$ a linear subspace
of the 1-homogeneous component $\mathcal{E}_{1}$ and any ideal $I_{[j]}$ of
$\mathcal{E}$, satisfying $\{I_{[j]},\mathcal{E},I_{[k]}\}
=\{I_{[j]},I_{[k]},\mathcal{E}\}=\{\mathcal{E},I_{[j]},I_{[k]}\}=0$ if $[j]\neq
[k]$, where the relation $\sim$ in $\sum^{1}=\{g \in G \setminus \{1\} :
L_{g}\neq 0\}$, defined by $g \sim h$ if and only if $g$ is connected to $h$.
