Photoinduced hole transfer dynamics from single CdSe/CdS(3ML)/CdZnS(2ML)/ZnS(2ML) core/multishell quantum dots (QDs) to phenothiazine (PTZ) molecules were studied by single QD fluorescence spectroscopy to investigate the static and dynamic heterogeneities of the hole transfer process as well as its effect on the blinking dynamics of QDs. Ensemble-averaged transient absorption and fluorescence decay measurements show that excitons in QDs dissociate by transferring the valence band hole to PTZ with a time constant of 50 ns for the 1:1 PTZ-QD complex, and the subsequent charge recombination process (i.e., electron transfer from the conduction band of the reduced QD to oxidized PTZ to regenerate the complex in the ground state) occurs mainly on the 100 to 1000 ns time scale. Single QD-PTZ complexes show pronounced correlated fluctuations of fluorescence intensity and lifetime with time. In addition to the dynamic fluctuation, there are considerable heterogeneities of average hole transfer rate among different QD-PTZ complexes. The hole transfer process has little effect on the statistics of the off-states, which is often believed to be positively charged QDs with a valence band hole. Instead, it increases the probability of weakly emissive or "gray" states.