Airbus Girl
In the UK, the only response from ATC to a TCAS RA call should be "C/S roger".
It used to be "C/S roger, report back under my control" but this was changed recently.
The pilot is supposed to report to ATC when the RA action is complete.
ATCOs become passengers when a TCAS RA is anounced, some used to try to 'assist' by giving instructions in the horizontal plane, but that is frowned upon now as it could detract from the TCAS action and may even reduce the effectiveness of a climb/descent.
sapperkenno
With regards to ATC taking less interest in their job because aircraft have TCAS - nothing could be further from the truth!
TCAS is a last resort safety measure, in fact I have seen replays of a couple of instances where TCAS in the LTMA has caused one incident to escalate and cause multiple losses of seperation.