Jeff,
The 'local' ATC station is responsible for airborne traffic and must
provide 'standard' separation but ACTUAL avoidance is always the first
responsibility of the pilot. They may give advisories and often do but it
is only required when conditions permit.

Once traffic has been pointed out to you and you acknowledge having the
traffic in sight, ATC does not need to advise you ever again. Consequently,
there are times when it is to your advantage
not to tell ATC that you have the traffic.

Happened to me once when ATC told me of a KC-10 on short
final to a runway. I said I had it in sight. What I didn't know was that
it was a touch-and-go and not a full-stop. A bit later it filled my
windshield but ATC he don't say nothin'.
Gene