This paper indroduces space-parallel transient stability simulation (TSS) solver tailored for large-scale Node-Breaker (NB) power system models using the Multi-Area Thevenin Equivalents (MATE) framework. The proposed approach features a distributed Sparse Tableau Approach (STA) enabling efficient breaker-level substation modeling without explicit topology processing, development of MATE equations for NB models, mapping matrices to formulate MATE based network equations for NB models and a weighted graph partitioning technique to ensure balanced parallel workloads. By exploiting both space and task parallelism, the solver achieves time efficient performance even with NB model matrices up to 50 times larger than their Bus-Branch (BB) counterparts. Extensive tests on the Polish 2383-bus, Pegase 9241-bus, and Pegase 13651-bus systems, each configured with Breaker-and-Half schemes, demonstrate execution times of only 2.8s ∼ 3.3s, 23.5s ∼ 28s, 30s ∼ 34.6s respectively for a 10s run on a 64-core, 2.2 GHz, 256 GB RAM compute node. These results establish the proposed MATE-NB solver as a scalable, high-fidelity, and computationally efficient solution for TSS of large-scale NB networks.