About your suggestion of unexporting the object..This would then render the object incapable of accepting any future rmi calls unless you export the object again.
What I want to know specifically is not to unexport but to stop it running after initial activation due to the first rmi method call.....
use the activatable.inactive() method, this will export the object if its not currently in use. And it will reactivate if there is another call for it after this.
I suggest putting this in a thread as the above will not deactivate it if it is in use.
see http://java.sun.com/j2se/1.3/docs/api/java/rmi/activation/Activatable.html for more info.