Concurrent Greenberger–Horne–Zeilinger (GHZ) distribution creates contention for finite Bell-pair resources whose availability is revealed only after probabilistic link generation, but constructing multicast trees after heralding is computationally expensive relative to the short lifetime of the generated entanglement. We consider a batch of GHZ requests that is known before link generation and served within a single time slot. We propose Predictive Multi-Tree Allocation (PMTA), which moves candidate-tree construction and joint capacity planning to a pre-heralding planning phase. This phase builds several approximate Steiner trees per request and solves an integer tree-packing problem for per-request copy budgets. A post-heralding adaptation phase transfers each budget among feasible planned trees and further allocates residual resources using a multi-request adaptation of multipath packing. Simulation results on 50-node Waxman-model networks (Waxman-50) show that PMTA consistently outperforms both Single-Tree Planning (STP) and Reactive Tree Allocation (RTA), with statistically significant gains over RTA. At 20 requests, PMTA improves mean GHZ throughput by 45.2% over RTA.

Quantum network,entanglement routing,GHZ- state distribution,quantum multicast,Steiner tree