a self that is necessarily dependently originated, although it doesn't really absolutely exist, still has the quality of existance (this apples to all compounded things that are born)
annihilationism and eternalism pertain to the nature of the self, which of course neither are true
but this does not preclude the possibily of a continuation of a particular aggregation of non-physical dependently originated consciousness.
i did some more research mr secular buddhist? if so, talk about an oxymoron.