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A bottleneck narrowing the development of large-scale integrated circuits (LSI) is the soaring demand for cooling capacity. Since researches on the manifold micro-pin-fin heat sink (MMPFHS) indicated the superiority of discretized hot spot area, good scalability, and low thermal resistance. As an emerging heat sink structure design, the 3-D flow organization of MMPFHS is determined by 2-D tiling pavement of micro-pin-fins and nozzles. This concept combines the tiling geometry and heat transfer design, which offers a new idea for high heat flux cooling applications. The present study focuses on the MMPFHS of irregular topologies, including quadrilateral topologies (QTs) and hexagonal topologies (HTs). Actually, the irregularity of topologies can also be presented by the bias of inlet positions. The results revealed that the biased inlet greatly influences the heat transfer of the QTs' lateral conjugate surface and the HTs' bottom conjugate surface. Among the topologies, regular-QT shows the lowest total thermal resistance R tot of 0.0984 ×10−4 Km2/W at D PF = 112 μm and D N = 56 μm. For the RMSE of the maximum temperature initiated by irregularity, QTs are lower than HTs, indicating that the heat transfer performance of QTs is stable under irregular topologies. • Irregular polygon topologies of MMPF heat sinks are proposed and discussed. • Hydrodynamic and thermal performance of the irregular topologies is analyzed. • Geometric parameters and operating parameters are investigated considering irregularity. • Hexagonal topologies are more influenced by irregularity than quadrilateral topologies. [ABSTRACT FROM AUTHOR]