How do controllers coordinate clearances through sectors?

I'm curious, how does one controller secure a direct clearance through
mulitple other controllers' areas? Sometimes it seems that after a
handoff the receiving controller doesn't know what your clearance is
(but certainly must have that area available for you).

As a typical example, I was flying home from Monterey last night and,
after passing the San Jose arrival area, received an updated
clearance, direct to my destination. Two controllers later, the
controllers asked me if I was direct to the VOR. I said no, I'm direct
home.
I'm curious how the issuing controller is able to ensure a clearance
all the way home direct. And how is it that a receiving controller
doesn't know what a plane's current clearance is? Doesn't this all
make it hard to plan conflict free traffic???

Do controller's "own" their own areas or does the computer? Can the
computer approve a clearance through a controller's area w/o his
acknowledgement? Does a controller need the computer to approve what
he does in his area?

-Robert