  We study the entangling properties of multipartite unitary gates with respect
to the measure of entanglement called one-tangle. Putting special emphasis on
the case of three parties, we derive an analytical expression for the
entangling power of an $n$-partite gate as an explicit function of the gate,
linking the entangling power of gates acting on $n$-partite Hilbert space of
dimension $d_1 \ldots d_n$ to the entanglement of pure states in the Hilbert
space of dimension $(d_1 \ldots d_n)^2$. Furthermore, we evaluate its mean
value averaged over the unitary and orthogonal groups, analyze the maximal
entangling power and relate it to the absolutely maximally entangled (AME)
states of a system with $2n$ parties. Finally, we provide a detailed analysis
of the entangling properties of three-qubit unitary and orthogonal gates.
