Asteroids are generally pretty massive rocky bodies if a comet collided with one there'd be a pretty big bang - In 1994 one collided with Jupiter
http://www.daviddarling.info/images/Jupiter_co metimpact.jpg
the red mark at the top is what happened at just one part of the impact.
If a comet passed through a lot of small asteroid pieces it would effectively get shot blasted to pieces. That would look very pretty in the night sky I'd think.
Comets get smaller every time they get close to the sun, the tail we see is them loosing matter as the sun heats them up and the solar wind pushes out the tail so the largest ones will not be periodics like Halley that regularly revisit.
Good question about the maximum size - here's an answer from the web (I won't pretend I knew before I looked)
http://www.newton.dep.anl.gov/newton/askasci/1 995/astron/AST147.HTM
Comets are believed to be composed of the debris from the early formation of the solar system. When the sun ignited most of this matter was blown away into regions beyong pluto known as the Kuiper belt and the Oort cloud. Sometimes objects out there nudge each other and end up in an orbit bringing them in towards the sun and they end up as comets, some get into eliptical orbits and end up revisiting, others only make it in once.
We're begining to find out much more about the space past Neptune, there even seems to be 'planets' there like Sedna and at least one larger than Pluto
http://www.nineplanets.org/kboc.html