  We devise the optimal form of Gaussian resource states enabling continuous
variable teleportation with maximal fidelity. We show that a nonclassical
optimal fidelity of $N$-user teleportation networks is {\it necessary and
sufficient} for $N$-party entangled Gaussian resources, yielding an estimator
of multipartite entanglement. This {\it entanglement of teleportation} is
equivalent to entanglement of formation in the two-user protocol, and to
localizable entanglement in the multi-user one. The continuous-variable tangle,
quantifying entanglement sharing in three-mode Gaussian states, is
operationally linked to the optimal fidelity of a tripartite teleportation
network.
