Abstract: In this talk I present a problem that is still bugging me, but which I hope to clear before finish writing the thesis. It looks like the Hilbert-Samuel functions for Z-graded superrings admit a feature that commutative rings don't show: they can have two poles! I will deduce this in the talk and then present some example..., which will show that I cannot find examples with this feature. All are invited to take a critical look!