You don't want to bother your AdminCc with every little details once someone takes ownership, so you don't want to add "On Correspond Notify AdminCcs".

This scrip will only send correspondance if the ticket isn't yet owned.

Condition: User Defined

Action: Notify AdminCcs

Template: Global template: Admin Correspondence

Custom condition:

my $trans = $self->TransactionObj;

return 0 unless $trans->Type eq "Correspond";
return 0 unless $self->TicketObj->Owner == $RT::Nobody->id;
return 1;