Open dist/DoPluginApp.html to see a page with plugin.

On that page click "Init". A window appear. It is of none-modality option and has a parent - the primary stage.

In appeared window click "APP" this will create and application_modality child and the previous will be a parent.

In appeared window uncheck "create new with this as parent" and click "NONE". This will create a new window which doesn't have this as parent and the new window will be of none-modality type.

In new window click "WIN" without unchecking of "create new with this as parent" (I mean, a new must be created as child and checkBox must be checked.)

Thus, we have two hierarchies: three windows are in the first (primaryStage(NONE), stage0(NONE), stage1(APP)) and two are in the second (stage2(NONE), stage3(WIN)).

You can see that if you click on primaryStage of applet, or on the first or the second green stages, then the last two windows will disappear (z-order will put them under applet stage). If you click on java application in task bar then the last two windows will apear.

To compile applet:

In build.xml change classpath="C:/work/builds/b46/javafx-sdk2.0/tools/ant-javafx.jar"/> on yours.
and press "clean and build" on project.
In dist you could find all compiled files.