Of course, there are exceptions. In these cases you will need to do some detective work.
If the website has its own domain name, such as "example.com" (for www.example.com), you can make a start on tracking down that information by performing a "whois search" for the domain name of the site. There are many websites available that provide free whois searches; the preceding link is just one of them. A whois search will tell you who registered the site, and who the technical contact persons are. You can then attempt to contact those individuals. If they are not responsive, which is not uncommon due to the large quantity of spam emails received by addresses in the whois database, you should also look at the "domain servers" or "DNS servers" listed at the end of the whois information. These are the computers responsible for giving out the IP address of the website; they should belong to the hosting company, or to the parent company of the hosting company. This will usually give you the name of the hosting company, and you can then visit their site and make contact with them. When the owners of a website do not wish to be identified this is often the only method that works.
If the website is hosted for free through a service like Angelfire or Geocities, you will be able to determine this right away from the address of the site, which will end in geocities.com or similar, rather than a domain name registered specially for the site. In these cases, you can visit the website of the free hosting service in question to seek more information about the owner of a particular account. Of course, not all such services will give out information about the owners of their pages unless legally compelled to do so.
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