While the International Festival has its global reach built into its name, and departing director Jonathan Mills has extended its reach as an Australian might have been expected to do, the Fringe has been no less concerned to grow its international reputation in recent years.
Perhaps that is to put the development the wrong way around, though, because what has happened has been a huge increase in the number of performing companies coming to Edinburgh with the support of their local governments.
So while the Georgian and South African contigents that have been an established part of the Assembly Theatre programme for many years were brought by enthusiastic and driven individuals, the high profile of Polish work last year, and companies from Brazil, Macao and New Zealand this year, to name just three of many, come with crucial government support.
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They want an audience, of course, but the message is as much about exporting the culture.
The New Zealanders are a major presence this year, with shows that celebrate the haka that we know from the rugby field, and an interactive zombie invasion performance, dance and music on both the Festival and Fringe and a cluster of artists in the Edinburgh Art Festival.
Dick Grant, the chairman of the Arts Council of New Zealand, which also seems to be going through a rebranding exercise to become Creative New Zealand, told those who attended the NZ at Edinburgh launch showcase it was a "the largest group of leading New Zealand actors, dancers, musicians, visual artists, writers and Maori performing artists we have ever toured abroad".
"We see it as an extraordinary chance to show thousands of people who work in the world of the arts and culture the vibrancy and creativity of New Zealand and New Zealanders ... to bring our world to yours," he said.
A man who made the journey the other way 13 years ago is Stuart Clumpas, founder of DF Concerts and creator of T in the Park.
Glasgow-bred, he established the Dance Factory as a gig in Dundee before taking the brand Scotland-wide as a rock and pop promoter, leading to the first festivals in Strathclyde Park and then the transfer to Balado, as well as the creation of King Tut's Wah Wah Hut as an essential small venue in Glasgow.
He left Scotland and the music business behind and took his family to New Zealand. He has only recently returned to the business there, taking over the running of a vast Glasgow Hydro-style arena in Auckland that now gives New Zealanders a stop-over for artists like Beyonce and Katy Perry.
"The difficulty is in the logistics of getting people to pay for the air freight from Australia or America, so we are seeing lots of acts playing in New Zealand for the first time," says Clumpas.
After years away, during which he acquired a pilot's licence, became involved in aerial mapping, was a leading light of the NZ aircraft owners association and dabbled in motor racing as well as the occasional promoting project with acts including comics The Flight of the Concords, he sounds engaged with the old business. There is a 350-capacity venue attached to the Auckland arena that he sees as a possible NZ Tuts "for older punters".
"I find I'm enjoying myself at that kind of thing," he says.
Clumpas has a Westerner's perspective on the culture of New Zealand and he has thought about it a lot. He points out that even the indigenous culture is comparatively young. There is no trace of early human habitation in New Zealand as there is in the aboriginal heritage in Australia. Roman remains in Bearsden are 1,000 years older than archeology has found in New Zealand, he notes.
"There is such a Scottish influence here, much stronger than in Canada," he says, "and especially in the South island you can see it in the place names. There was a a lot of interaction between the Scots and Maoris in the early days and it has been handed down. You hear people say things like 'a wee bit' all the time, and there is something of the Scots in the Kiwi reticence, when compared with Aussie flamboyance. New Zealanders can be more circumspect and gulity of that tall poppy syndrome: just who do you think you are?
"But as far as influence from the UK is concerned, Scotland is the dominant culture, not England, by a factor of about two to one in terms of the family background of people."
"The arts in New Zealand are mostly about theatre and performing arts. They are not really strong in contemporary music. Although there are a lot of good solid rock and roll bands there just isn't the same level of acts, or even interest, and I don't know why.
"Perhaps people are just too happy here. New Zealand is a nice place to live in and what poverty there is is rural and not as grim. You don't need as much money and people don't have the angst, so song-writing is not at the same level,"
Clumpas points out that when Keith Richards of The Rolling Stones was hospitalised after falling out of a tree, he was left alone to recover. The story was a one-day wonder.
"There is no tribal tabloid press here and folk are really not obsessed with celebrity," he says. "Compared to Scotland I feel I am in a more comfortable place."
But if he were still in Scotland. how would he be casting his ballot next month?
"I'm a staunch federalist so while my head says to vote No, my heart says Yes. Devo-max should be on the ballot paper - the people of Scotland are being cheated not to be offered that. It is a political scam so people should boycott the vote - the majority are not being given the chance to vote for what they want most."