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When using CreatePalette[], the palette created always shows up on the upper left corner. Is there a way to make it show up at the center of the screen, just like what CreateDialog[] does?

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You need to change the preset value of the WindowMargins option to Automatic. Example:

 CreatePalette[Row[PasteButton /@ ToExpression[CharacterRange["a", "z"]]], 
 WindowMargins -> Automatic, WindowTitle -> "Letters"];
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