[Eonwe]

I'm pretty sure that the ringwraithers are attracted to the ring. Gandalf, or maybe the elf they meet before Rivendell, tells Frodo that they can sense the Ring and will therefore pursue him until they find it.

If I'm not mistaken, the Witchking has pressing business to attent, and Galadrial's phial has something to do with repulsing him or something or other.