Preheat the oven to 350°F. In a large bowl combine the apples, pears, apricots, cherries, granulated sugar, flour, lime juice, cinnamon, nutmeg, and allspice. On a large dry cutting board, place one sheet of phyllo dough, spray with a little nonstick spray. Top first sheet of phyllo with the second and third sheets, spraying cooking spray between each layer.
Working lengthwise with a paring knife, cut the stack of phyllo sheets equally into 4 strips. Divide the filling into 4 equal parts. Cover 3 of the phyllo strips with a damp cloth. Spoon ¼ of the fruit mixture in the center of one end of the remaining strip. Fold the right corner over to the left side, covering the filling. Continue to fold the strip, flag-style, in a triangle pattern until filling is completely enclosed. Repeat with remaining filling and phyllo strips.
Place triangles on a nonstick baking sheet and bake for 14-16 minutes, or until golden brown. Combine powdered sugar and milk until well blended; drizzle over warm turnovers.
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