Can I remove the SupaDupa branding from my online store?

There are possibly two parts to this question.
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If you are referring to the "mysupadupa.com" that appears in the URL, then yes you may purchase your own domain name and use that as the URL for your boutique instead.
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More likely, you are referring to the "E-Commerce By SupaDupa - Create Your Own Online Store" tagline at the bottom of your pages. Please see this article for information on how to do that: How to remove Supadupa Logo - de-badge credit at the footer
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