Full code after the jump.

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2008/04/06/centering-a-pop-up-window-when-a-flex-application-is-resized/ -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white"
        resize="application_resize(event);">

    <mx:Script>
        <![CDATA[
            import mx.events.ResizeEvent;
            import mx.controls.Alert;
            import mx.managers.PopUpManager;

            private var alert:Alert;

            private function init():void {
                alert = Alert.show("The quick brown fox jumped over the lazy dog.", "title");
            }

            private function application_resize(evt:ResizeEvent):void {
                if (alert) {
                    PopUpManager.centerPopUp(alert);
                }
            }
        ]]>
    </mx:Script>

    <mx:ApplicationControlBar dock="true">
        <mx:Button label="Launch!" click="init();" />
    </mx:ApplicationControlBar>

</mx:Application>

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Full code after the jump.

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2007/09/23/triggering-effects-when-a-container-is-resized/ -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white">

    <mx:Script>
        <![CDATA[
            private function sizePanel(w:uint, h:uint):void {
                panel.width = w;
                panel.height = h;
            }
        ]]>
    </mx:Script>

    <mx:Resize id="resize" />

    <mx:ApplicationControlBar dock="true">
        <mx:Button label="160x160"
                click="sizePanel(160, 160);" />
        <mx:Button label="240x160"
                click="sizePanel(240, 160);" />
        <mx:Button label="160x240"
                click="sizePanel(160, 240);" />
        <mx:Button label="320x240"
                click="sizePanel(320, 240);" />

        <mx:Spacer width="100%" />

        <mx:Label text="w:{panel.width}, h:{panel.height}" />
    </mx:ApplicationControlBar>

    <mx:Panel id="panel"
            title="title"
            status="status"
            width="320"
            height="240"
            resizeEffect="{resize}">
        <mx:Accordion id="accordion"
                historyManagementEnabled="false"
                width="100%"
                height="100%">
            <mx:VBox label="Shipping Information" />
            <mx:VBox label="Billing Information" />
        </mx:Accordion>
        <mx:ControlBar id="cb">
            <mx:Button />
        </mx:ControlBar>
    </mx:Panel>

</mx:Application>

View source is enabled in the following example.