On the public side, the links for the entries are created by the file /includes/functions.php After making a backup, you should be able to search for the word "target" and change the value, or remove it.

You might also want to check the files for whatever theme you use, but I'm not sure any "target" links exist there.

2 things to keep in mind.

Normally when you click a link to visit the URL of an entry, a small java script routine calls out.php?ID=X where X is the ID for the site, out.php then increments the outbound click count and redirects the browser to the URL for that ID. I'm unsure if out.php would need to be altered.

The destination site may have a breakout of frames javascript anyway.

Dont you think this solution will work Dew ? What else could be changed to keep the Links subdomain wrapped in a Joomla site?

I'm sure it can be made to work but I'm stuck in the 90s and as any caveman HTML coder knows frames are bad, so I've rarely used them, thus I really am not that familiar with how they behave.

The reason I avoid frames have to do with SEO, and search engine spiders.. I also don't really think it is polite to wrap frames around other others people content.. that just seems fundamentally deceptive to me.