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The effects of lead positions and lead-ring coupling regimes are investigated for spin-related transport through a twodimensional network of quantum nanorings (2DNQRs) considering Rashba spin-orbit interaction (RSOI) and magnetic flux. A matrix representation of the transmission and reflection coefficients through a single ring connected to the arbitrary number of leads has been introduced. As a specific example of 2DNQRs, the conductance, spin polarization and system efficiency are obtained via a triangular network of quantum rings (TNQRs). TNQRs are completely opaque or transparent versus RSOI strength and wave vector (k) of the incident electron. The periodicity of these functions along the k axis depends on the lead positions and is independent of lead-ring coupling. Also, the symmetric geometry and strong lead-ring coupling regime significantly improve the performance of the system as a multipurpose spintronic device (i.e., a perfect spin filter, spin splitter, spin switching, Stern-Gerlach device and an electronic switching device).