Popup dialogues on Mac OS X are typically implemented using sheets (http://developer.apple.com/library/mac/#documentation/UserExperience/Conceptual/AppleHIGuidelines/Windows/Windows.html#//apple_ref/doc/uid/20000961-TP9).

A sheet behaves like a document-modal Stage whose parent is another Stage, and contains things like an alert, a login dialogue, a file chooser dialogue, etc.

The API for dialogues in JavaFX should permit implementations for the Mac based on sheets. Access to sheets is platform-specific (i.e. Mac OS X only).

I suspect this is an issue that many people are aware of: I've submitted this simply for completeness.