I want register a domain under the .eu TLD, but I don't live in Europe [which is a requiriment to that].
I'd like to know if there is any website which register the domain on its name or any other solution.
You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:
- The Registry shall:
(b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
(i) undertaking having its registered office, central administration or principal place of business within the Community, or
(ii) organisation established within the Community without prejudice to the application of national law, or
(iii) natural person resident within the Community
I'm not aware of any official/legal way to achieve what you desire, neither of any 'grey hat' option to circumvent this restriction (though the latter
will likely be possible somehow as usual seems indeed possible as per Joel Ethertons answer - make sure to read my comment as well though ...).
So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).
Go grey hat with Network Solutions. They provide proxy EU registrations through their affiliate corporation: http://www.networksolutions.com/support/registering-eu-domain-names-2/
If you live outside Europe my company can do this for you for 18€ / year :) But with a minimum of 3 years.
Anyway if you look on Google there are dozens of registrars that can do this.