  We prove that for an open domain $D \subset \mathbb{R}^d $ with $d \geq 2 $ ,
for every (measurable) uniformly elliptic tensor field $a$ and for almost every
point $y \in D$ , there exists a unique Green's function centred in $ y $
associated to the vectorial operator $ -\nabla \cdot a\nabla $ in D. In
particular, when $d > 2$ this result also implies the existence of the
fundamental solution for elliptic systems, i.e. the Green function for $
-\nabla \cdot a\nabla $ in $ \mathbb{R}^d $. Moreover, introducing an ensemble
$\langle\cdot \rangle$ over the set of uniformly elliptic tensor fields, under
the assumption of stationarity we infer for the fundamental solution $G$ some
pointwise bounds for $\langle |G(\cdot; x,y)|\rangle$, $\langle|\nabla_x
G(\cdot; x,y)|\rangle$ and $\langle |\nabla_x\nabla_y G(\cdot; x,y)|\rangle$.
These estimates scale optimally in space and provide a generalization to
systems of the bounds obtained by Delmotte and Deuschel for the scalar case.
