I have a web site -www.example.com :
[MOD] Link removed [/mod]

are -www.example.org and example.org two different websites for google and just one???

Should I link the website with one same URL or both???

Please help me understand.

Well, -www.example.com is a genuine sub-domain of example.com, it's just the default one used in most cases.
Usually it is set to match the same folder as the main domain (example.com) and that's why it can create some confusion for Search Engines.

Because -www.example.com/a-page.html is a duplicate of example.com/a-page.html and basically all -www.example.com/ is a duplicate of example.com/a-page.html

It's a major and very common SEO issue, the way to fix it is simple, choose one between the two and apply the www prefix redirection to make sure the one chosen and only it can be used. The other one will be HTTP 301 redirected, so that all links will always work and duplicates will, after a month or so, disappear from the SERPs (which is a very good thing).

Example :
http://phpbb-seo.com/boards/

Hi, I am currently using a template to manage my website.

Can you provide me with a custom html code to put in the HEAD to indicate my preferred domain. My prefered domain is domain.co.uk instead of -www.domain.co.uk

Things to to note:
I also have two separate blogs which are located on two separate subdomains:

news.domain.co.uk
filmreviews.domain.co.uk

Can you ensure the code will not conflict with my subdomains.

Thanks

You can use the canonical element : Nofollow links and canonical link element
But it's not as strong as the www prefix redirection.
About sub domains, it really depends on how are they installed, if they are installed in a separate directory (can be a sub directory) of your main domain, then you can implement the www prefix technique directly for each domain (method n°2 is preferred), otherwise, you will have to add RewrtieConds or use method n°1 and only make sure that example.com is not used, but -www.example.com or sub.example.com is.

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