This paper introduces the topology-independent distributed multichannel Wiener filter (TI-dMWF), a novel algorithm for distributed node-specific signal estimation in wireless acoustic sensor networks (WASNs) with unconstrained topologies. The TI-dMWF enables each node in the network to compute its centralized multichannel Wiener filter solution by exchanging only low-dimensional fused signals, without requiring iterative estimation, unlike state-of-the-art approaches such as the topology-independent distributed adaptive node-specific signal estimation (TI-DANSE) algorithm. The TI-dMWF is proven optimal when each source is observed by either all nodes or only one node. Theoretical analysis and numerical simulations confirm that it achieves centralized estimation performance in a single run. Its latency as a function of the pruned-tree depth and its computational complexity are also analyzed. Its robustness is assessed in reverberant-room simulations under estimated second-order statistics, various network topologies, and deviations from the assumed observability model.

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