This article presents a self-driven multi-heat sinks system suitable for cooling multiple heat sources simultaneously. This system can include one driving heat sink and multiple passive heat sinks. The porous medium inside the driving heat sink absorbs heat from its heat source, causing the working fluid to evaporate. The phase changing generating capillary force to drive the circulation of liquid throughout the system. The circulating working fluid flows through the fluid channels in the external passive heat sinks, carrying away the heat from the heat sources at each passive heat sink, thus simultaneously cooling multiple heat sources. This study primarily altered the connections between heat sinks, specifically connecting them in serial and parallel, forming systems with different structures. The operating characteristics of the two differently structured systems were studied through experiments. Results show that both systems effectively dissipate heat, maintaining stable operation at a maximum heat load of 100 W. By comparing the operating characteristics of each heat sink in different structures, it was found that the structure mainly affects the circulation resistance of the working fluid. In the serial system, the high circulation resistance leads to long startup times and high startup temperatures. In contrast, the parallel system effectively addresses these issues and, due to its lower internal circulation resistance, and reduces the operating temperature of the driving heat sink. The parallel system's startup time and temperature are 7% lower than the serial system, and its driving heat sink can handle an additional 10 W of heat load. However, due to the structural impact, each passive heat sink in the parallel system receives lower flow, resulting in higher operating temperatures for the passive heat sinks. Based on the research findings above, the article concludes by outlining the suitable operating conditions for different systems: series-connected and parallel-connected systems are respectively suitable for scenarios where the heat generation of multiple heat sources is similar and where it varies significantly.