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Presently, a major of detectors for PET systems are based on scintillator crystals read by photomultipliers. In our previous work, a very good time resolution recorded with a 10x10x5 mm3 LSO crystal coupled to a Photonis XP20D0 and Hamamatsu R5320 photomultipliers was shown. Results for both detectors were almost identical and close to 170 ps but their properties such us quantum efficiency of the photocathode and time jitter were significantly different. The XP20D0 possessed high QE and the measured photoelectron number was 40% larger than that of R5320. The R5320 had a time jitter of 140 plusmn 7 ps at FWHM, three times better than that of XP20D0. The fact, that despite of large differences in parameters of the used PMTs a comparable time resolution was achieved, triggered our further study of the most important properties of the photomultipliers and their influence on timing and energy resolution towards to optimize TOF PET systems. Thanks to a close cooperation with Photonis, during last few years we gathered a large amount of information and experimental data of various types of PMTs. The aim of this paper is to present general conclusions and dependencies that were derived from these multiple experiments. This should help to develop an ultimate, PMT based detector, for TOF PET systems.