By the book , JAA allow one with 1500hs to ship an airliner.Once you have your ATPL , theoreticaly you are already allowed to be Captain of an airliner.
I`ve seen some guys on the left that I wouldn`t release for the right seat.
In Europe ,instructors are "forced" to cause no problems releasing pilots for both left and right seats in order not to cause problems to the company and this way keep their function as instructors.
Nowadays most instructors must be nice guys if they want to take some extra $$ home.