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Electron-positron pairs' generation occuring in the interaction of$10^{18}$-$10^{20}$~W/cm$^2$ laser radiation with high-Z targets are examined.Computational results are presented for the pair production and the positronyield from the target with allowance for the contribution of pair productionprocesses due to electrons and bremsstrahlung photons.  Monte-Carlo simulations using the PRIZMA code confirm the estimates obtained.The possible positron yield from high-Z targets irradiated by picosecond lasersof power $10^2$-$10^3$~TW is estimated to be $10^9$-$10^{11}$

Estimates of electron-positron pair production in the interaction of high-power laser radiation with high-Z targets