Is it possible to host a site under a registered domain name on a free hosting service?
Or do you always end up having to use the hosting site's domain name as a prefix.

Alot of free hosts allow you to use your own domain, with the option of using theirs.

I've looked a lot around the net and the free hosting sites all seem to charge you to transfer your domain. I'm not against paying but I wonder if it is possible to find a free host that will transfer your domain without charging you. I'm not expecting much viewing of my site.

Hosts will charge you for transferring a domain name. Transferring means that they will tack on another year to the registration and they will manage your domain, or give you control for you to do it. The host then becomes your registrar.

But, if you have a domain registered with, say, godaddy... you do not need to transfer it to a host to use it. All you need to do is get the nameservers of your host and use godaddy's control panel to enter those nameservers. This will point your domain to your site.

Most free hosting companies now allow you to point your domain to your account with them. This should not be confused with transferring your domain to them.

You could just use your registrars domain forwarding feature (usually free) to send all web traffic for domain.com to http://freehost.com/~username/

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Yes, sure, we will host your domain at pt-web.net

I suggest using a redirect, simply redirect your domain name to your free hosting. Many people use .tk domain names, just a suggestion.

yes, but redirections are always slow...