For positron emission tomography (PET) online data acquisition, a centralized coincidence processor (CCP) with single-thread data processing has been used to select coincidence events for many PET scanners. A CCP has the advantages of highly integrated circuit, compact connection between detector front-end and system electronics and centralized control of data process and decision making. However, it also has the drawbacks of data process delay, difficulty in handling very high count-rates of single and coincidence events and complicated algorithms to implement. These problems are exacerbated when implementing a CCP on a field-programable-gate-array (FPGA) due to increased routing congestion and reduced data throughput. Industry companies have applied non-centralized or distributed data processing to solve these problems, but those solutions remain either proprietary or lack full disclosure of technical details that make the techniques unclear and difficult to adapt for most research communities. In this study, we investigated the use of a set of distributed coincidence processors (DCP) that can address the CCP problems and be implemented relatively easily. Each coincidence processor exclusively connects one detector pair and selects coincidence events from this detector pair only, which breaks a centralized coincidence process to a collection of independent and parallel processes. DCP can significantly minimize the data process delay, maximize count-rates of coincidence events and simplify implementation by implementing a single coincidence processor with one detector pair and replicating it to the rest. A prototype DCP with 42 coincidence processors was implemented on an off-the-shelf FPGA development board for a small PET with 12 detectors configured with 42 detector pairs. DCP performances were tested with both pulsed signals and gamma ray interactions. There was no coincidence data loss up to the detector's maximum singles count-rate (250 k s-1). Approximately 1.2 k registers were utilized for each coincidence processor and the FPGA resource utilization was proportional to the number of coincidence processors. Coincidence timing spectra showed the results from accurately acquired coincidence events. In conclusion: complementary to CCP, DCP can provide high count-rate capability, with a simplified algorithm for implementation and potentially a practical solution for online acquisition of a PET with a larger number of detector pairs or for ultrahigh-throughput imaging.