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How do I unlink the tags?

Use <?php ctl_the_tags('Tags: ', ', ', '', false); ?> instead of <?php the_tags(); ?>.

How do I use a custom taglink?

You can use, for example, <?php ctl_the_tags('Tags: ', ', ', '', true, 'http://www.technorati.com/tag/%tag%'); ?>.

My custom taglink does not work.

The function does not check whether the taglink you entered is valid or not. Be sure to inclue %tag% in the taglink to ensure that it can be replaced by the actual tag.