And then once you cross an ocean, it's even messier. There have been complete copies of Broadway productions overseas...scenery, costumes, lights, choreography, blocking, etc... that have no offiliation with the original licensing, but since it's in a different country, there's not much we can do over here.
In Australia it may be slightly different. We have a large population, but a very small theatre market: what this means is that if you're in a large city, and most here are, you will have very quick saturation of your target audience. Ie. Mamma Mia will have been seen by the majority of theatre-goers no matter which capital city you perform in.
This has a knock-on effect in that it raises interest in local amateur performances of the same show; but it also means that you'll find it difficult to perform something amateur-wise that rips off from professional productions. It would be very easy to notice: and it is. Local amateur groups get caught out all the time using unlicenced music/scripts. People here from the relevant organisations do check these things out.
I think though that most local amateur groups here - the established ones - are more likely to pay royalties, not just because they can afford them, but because they respect the artists. Unfortunately, where I think it goes haywire is in the local independent/fringe (what you Americans would consider off-Broadway) groups are somewhat less respectful. But then, they tend to produce things that no one has heard of, and are not likely to be caught out copying Mamma Mia but rather some indie band's latest song.
Sadly, I know of one specific case where our national opera company (basically the only professional opera company in Oz) completely ripped off a well-known movie. See the blog/video I posted last year on my site:
http://www.puppetsinmelbourne.com.au/blog.php/2010/08/30/pirated-piratesDespite being easily noticeable as ripping off something, they don't seem to have suffered any repurcussions. Maybe they got permission, but I think it's poor form for an opera company to trade on this.
I'll also note that your Broadway productions are pretty much what our Australian theatre audience will see at any given time. Getting them to - even an Australian well-known - original Oz works is near impossible. The only thing that is Australian about the show is the cast; because local producers are required to use everything that overseas designers created, from choreography to lighting design. I doubt that major producers would risk losing rights to a money-making show (the only ones that make any money are Broadway imports); so any breaches of copyright are more than likely going to come from amateurs.
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