You don't have to make the method static; doing so would likely be useless, as you'd want the method call to do something with the component's current state, I'm guessing -- use some of its data, change its appearance, etc. What you really need is an object reference.
Since Application.application resides at the top (or actually very close to the top) of the fabled Display List, you should be able to access each component by starting at that point and then traversing the Display List -- until ultimately, upon arriving at your nested component, calling its publicly defined method.
However, I must say (with the utmost respect!) that you're venturing into dangerous OO waters, here. :) The right way to do this would really be to figure out some way to pass a reference to your custom component to the ActionScript class that requires access to it -- for example, in your MXML:
<mx:Script>
<![CDATA[
private function this_creationComplete(event:Event):void
{
var yourObject:YourClass = new YourClass(yourCustomComponent);
}
]]>
</mx:Script>
<components:YourCustomComponent id="yourCustomComponent" />
... and then in your ActionScript class:
public class YourClass
{
private var componentReference:YourCustomComponent;
public function YourClass(component:YourCustomComponent)
{
this.componentReference = componentReference;
}
private function yourMethod():void
{
this.componentReference.someMethodDefinedInYourComponent();
}
}
An approach like that would probably serve you better. Does it make sense? I'll keep an eye our for comments; post back and I'll do my best to help you through it.
Take a look at using the PopUpManager. That will allow you to place the TileList so that it floats above other components when it's placed on the stage. You'll still need to figure out where to position it on the stage, but you can use the localToGlobal() and globalToLocal() methods to help you position the popup TileList.
Best Answer
Below is one way that you can listen to the change of TileList.selectedItem. I would recommend against putting this in a global variable, although if you must you could use a pattern like ModelLocator to do so.