Dennis, to be honest I do not enter many competitions and certainly cannot categorically state to be aware of any EU wide competition, this does not however prove there have not been any. Many large companies split their marketing within the EU across different countries; for instance Nikon UK, markets Nikon Equipment in just the UK and Ireland, the rest of the EU is covered by other Nikon HQs; PepsiCo similarly has different marketing strategies, from its different EU departments. Also, there are indeed some regulations that would have to be complied with, for instance I believe, within the EU, that there has to be a skill question involved, to prevent the promotion being labelled a 'lottery'. Most EU countries also insist that promotions (including terms and conditions) must be advertised in the local language. Therefore, with my very inadequate linguistic skills, it would be hard for me to determine whether any similar looking marketing campaign across 2 or more countries, is indeed the same competition.
As for whether Taylor would do it as long as it were practical, I do not know. I do know that they do not market the full range of Taylorware clothing within Europe; even the people I have spoken to in Amsterdam do not know why some items are not sent to them. However, I always attend the Roadshows held in my area and will ask at the next one regarding competitions and see what the answer is.