Ok, this is not as much as a theory as a suggestion. In fact, I do not believe it myself. I just read Tamyrlin's theory on Lanfear and the Seanchan, and it got me thinking( great theory tam!). My suggestion is that maybe (really big maybe) Lanfear is masquerading as Alivia. I believe that Tamyrlin is right in assuming that Lanfear was with the Seanchan for a time, and in order to fit in with the Seanchan, you must know their ways well. That is why she can pretend to be Alivia. We also know that Lanfear is a great actor, from her performance with Asmodean in the waste, and that she's not afraid to be someone very unlike herself(old or fat).

This also gives a good reason why Min says that Alivia will "help destroy him" or something like that, and this can be done in two ways: she could kill him, which is unlikely; or help him against the Dark One( something i think Alivia will do, whoever she is).

I, like Tamyrlin, think that Lanfear might be necesary to seal the bore, because she is the one who drilled it in the first place. This would also be the reason for Alivia's great power.

Now, for the many implications to this theory. One, why would Lanfear fake not knowing how to use the op in many ways, especially against Graendal(or Cyndane, whoever it was she fought in WH) when it could be a life or death situation? Why, really, doesn't she just kill Rand right away, because now she hates him? And how does this fit in with the situation with her, moiraine, and the finns? As you can see, there are many implications with this theory( and many more than what i listed). Feel free to find more problems and tare this theory to shreds.