After getting no concrete help from shopify help desk and getting the same *wrong answer* to be found on on various sites, we found a quick hack that is able to canonicalize your domain url so that you won't have any strength dilution.

Same that hasn't being properly documented yet, hence the need to spread the word.

  • go to /admin/settings/domains
  • click on the www version
  • tick  Redirect all traffic to this domain This will redirect traffic from all your domains to the single primary domain.

Job done.