UK interest
"Today, Europe's competitive knowledge society becomes very visible to the world on the internet," said the EU Information Society and Media Commissioner Viviane Reding.
"Europe and its citizens can now project their own web identity, protected by EU rules," she said.
According to the .eu administrator Eurid, German and British net users account for most of the domain name applications.
British registrants made up 236,573 by late afternoon, just behind Germany with 237,928.
In third place were the Dutch with 125,426 applications.
"The new .eu domain name will become second only to .com in terms of importance and the volume of traffic that the best .eu domains are likely to attract," said Markus Eggensperger, legal and PR director for domains for web portal Lycos.
"British applications have been flowing in thick and fast as internet users battle it out to get hold of the best names.
"As a result of this, we expect there will be a lot of trading in the new domains as opportunists snap up the best names and offer them for sale on the open market," he added.
Conflicting claims
Backed by the European Commission, the .eu domain is intended for organisations and people based in the 25 nations of the trading bloc.
More than 1,500 firms have signed up to sell the .eu domains at prices ranging from 12 to 100 euros.
The sunrise period was run in two stages. For the first two months from 7 December 2005, public organisations and trademark holders could apply.
On 7 February those who had owned "other rights" could apply and all EU citizens get the chance from 7 April.
During the sunrise period, more than 335,000 applications were received and 95,000 of those are known to involve conflicting claims for domains.
For instance the www.polo.eu domain was applied for by car maker Volkswagen, fashion house Ralph Lauren and sweet maker Nestle. The domain has been awarded to Volkswagen which got its application in first.
Similarly, the Discovery Channel has won control of www.discovery.eu beating Land Rover by a number of minutes.
Speculators who are applying for the most coveted domains could also have a tricky time securing a name. The system is run on a first-come, first-served basis.
For instance, there are more than 280 applications to control the www.sex.eu domain, 220 of which were filed on the same day.
Many of these applications have expired because of missing paperwork, but it could take time to work out who has the best claim to generic and potentially profitable domains.
Thousands of domains of relevance to the European Commission have been reserved and cannot be bought by anyone else.