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Plasma mediated ablation of collagen gels and porcine cornea was studied at various laser pulse durations in the range of 1 ns-300 fs at 1053-nm wavelength. It was found that pulsed laser ablation of transparent and weakly absorbing gels is always mediated by plasma. On the other hand, ablation of strongly absorbing tissues is mediated by plasma in the ultrashort-pulse range only. Ablation threshold along with plasma optical breakdown threshold decreases with increasing tissue absorbance for subnanosecond pulses. In contrast, the ablation threshold was found to be practically independent of tissue linear absorption for femtosecond laser pulses. The mechanism of optical breakdown at the tissue surface was theoretically investigated. In the nanosecond range of laser pulse duration, optical breakdown proceeds via avalanche ionization initiated by heating of electrons contributed by strongly absorbing impurities at the tissue surface. In the ultrashortpulse range, optical breakdown is initiated by multiphoton ionization of the irradiated medium (six photons in case of tissue irradiated at 1053-nm wavelength), and is less sensitive to linear absorption. High-quality ablation craters with no thermal or mechanical damage to surrounding material were obtained with subpicosecond laser pulses. Experimental results suggest that subpicosecond plasma mediated ablation can be employed as a tool for precise laser microsurgery of various tissues.