[Morwen]

Well we'll have to agree to disagree.

Of course the sword is significant to Aragorn's personal tale. I've never said that it wasn't. I just don't believe that this can be treated as definitive proof that during all the years of his travels he must have taken the sword with him everywhere.

I also don't think that the "Bilbo hands over the Ring" comparison is apt. It is important, inevitable that the Ring must leave the physical custody and safekeeping of one bearer and go to another. The new Ringbearer has to become the Ring's physical custodian.
Aragorn having physical custody of the sword is not important in the same way. To me, what was more important on the day that Elrond "delivered to him the heirlooms of his house" was the revelation of his true name and "who he was and whose son". It is that knowledge, not the possession/custody of objects, that makes Aragorn take responsibility on his self and what prompts him to his subsequent deeds.
I therefore disagree that in the aftermath of Elrond's revelation to Aragorn that Rivendell is no longer the place for the heirlooms (ring and sword). In my opinion, the physical location of those objects isn't the point of the revelation. From that day forward Aragorn may certainly do with them as he pleases. But, Elrond isn't after all telling him to take his things and go.