You would use the resize event of the stage.
http://livedocs.adobe.com/flex/201/langref/flash/display/Stage.html#event:resize

Make sure the scaleMode has been set to StageScaleMode.NO_SCALE. Then in the
resize handler you would move your mc based on stage.stageWidth and
stage.stageHeight. (probably setting the mc's position to those values
halfed for x and y respectively)

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I am creating an AS3 application with a dynamic layout. i am having trouble
with making an mc stay in the center of the flash document even when the stage
is resized. does anybody know how to do this?

thanks