The weird thing is, for me, that I can have a favorite character to watch - I'll often have a particular favorite that I'll like their relationships with a whole bunch of other characters, and will also want to see building new relationships (the Doctor comes to mind). Often for me that favoritism gets bound up in a crush on the actor, so that I'll want to see them in everything, playing opposite anyone (as with DH now).

But when it comes to reading and writing, it's the relationships that grab me; I rarely want to read the character on their own. And it works in reverse - I'll have a favorite character, but when I start reading fic about them, I'll start to gravitate to particular relationships, until when I watch the show I'll prefer those relationships above any others (such as with SGA; originally I just liked Rodney, period; now I have a definite preference for Rodney-John and Rodney-team, over anything else.)