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We demonstrate the fabrication of graphene-deposited tapered fibers (GDTFs), which can be used as saturable absorbers (SAs) for pulsed lasers. The advantages of GDTF SAs include flexibility, all-fiber configuration, and high optical damage threshold. The fabrication process is based on the interaction of the evanescent field of a tapered fiber with graphene. By in situ monitoring the transmitted power, the deposition process can be controlled, and the GDTF with a desirable level of nonsaturable absorption loss can be fabricated. We also study the dynamic deposition process by employing different waist diameters of tapered fibers and the different deposition powers. The results show that the deposition time can be significantly shortened with stronger evanescent field by decreasing the taper diameter or increasing the deposition power. Furthermore, by exploiting the GDTF as an intracavity passive power modulating element, we demonstrate efficient Q-switched and mode-locked erbium-doped fiber lasers, respectively.