garbage collector frees and returns memory back to the heap, not "RAM". http://en.wikipedia.org/wiki/Java_Virtual_Machine_heap
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When does the garbage collector does it's work?
Whenever it feels like doing so. Perhaps never.
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Will I get a message saying "I'm being destroyed" after I give that object's reference a null pointer?
You will get a message when the garbage collector cleans up that space. Setting a pointer to null will not immediately trigger anything. It might never run; see point above.