  Multipartite quantum entanglement of a manybody is not well understood. Here
we numerically study the amount of tripartite Greenberger-Horne-Zeilinger (GHZ)
states that can be extracted from the state generated by random Clifford
circuits with probabilistic single-qubit projective measurements. We find a
GHZ-entangled phase where this amount is finite and a GHZ-trivial phase where
no tripartite entanglement is available. The transition between them is either
measurement-induced, at $p_c\approx 0.16$, or partition-induced when a party
contains more than half of the qubits. We find that the GHZ entanglement can be
enhanced by measurements in certain regimes, which could be understood from the
perspective of quantum Internet. Effects of the measurements to the growth of
GHZ entanglement are also studied.
