Hi Gail and Paul,
It's been said that JavaFX support multiplatform, and that JavaFX can use the full Java API, so, what happens when a JavaFX application that uses Java functions for desktop behavior it's tried to migrate to mobile devices? java desktop it's not the same for javaME.
You are right. The JavaFX mobile environment is a subset of the desktop environment. (Anything in the common environment will run in all 3 environments: desktop, mobile, and tv.)
NetBeans helps a lot here. If you write an application and deploy it to the Standard Execution, Web Start, or Browser anything in common or desktop will work. If you then change its execution environment to Run in Mobile Emulator, you will see source errors in the editor window for all references that are not in common (such as Swing components).
In NetBeans, right-click the project name and select Properties. Under Categories select Run. You'll see the Execution Model choices.