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We study the Schwinger effect in near-extremal nonrotating black holes in an arbitrary D(≥4)-dimensional asymptotically flat and (A)dS space. Using the near-horizon geometry AdS2×SD-2 of near-extremal black holes with Myers-Perry metric, we find a universal expression of the emission formula for charges that is a multiplication of the Schwinger effects in an AdS2 space and in a two-dimensional Rindler space. The effective temperature of an accelerated charge for the Schwinger effect is determined by the radii of the effective AdS2 space and SD-2 as well as the mass, charge, angular momentum of the charge, and the radius of the (A)dS space. The Schwinger effect in the asymptotically flat space is more efficient and persistent for a wide range of large black holes for dimensions higher than four. The AdS (dS) boundary enhances (suppresses) the Schwinger effect than the asymptotically flat space. The Schwinger effect persists for a wide range of black holes in the AdS space and has an upper bound in the dS space.