You post your Tumblr content on top of an existing theme, and the site offers hundred of available themes in its Theme Garden. While you can't have a Tumblr blog without a theme, you can replace the theme on your blog to change the way it looks. There's no way to delete a theme from the Theme Garden without reaching out to Tumblr.
Themes on the Blog
If you have a Tumblr blog, a theme is installed by default even if you've never selected one. Optica, the default theme, is a basic theme that offers many customization options and can take advantage of most of the integration that Tumblr offers with other programs. If you want to get rid of that theme or any other, you have to choose another Tumblr theme to replace it. If you're comfortable with HTML, you can change the HTML of any theme or create your own themes.
Replacing the Theme
To change your theme and replace it with another, sign in to Tumblr and then open your Tumblr dashboard. Hover over the upper right corner and click "Customize." Click "Browse Themes" to see the options. Each one you click is previewed so that you can see how it would appear on your blog. After you decide on the one you want to use, click "Use" and "Save" to replace your existing theme.
Themes in the Garden
If you've uploaded a theme to Tumblr's Theme Garden, removing it isn't as simple as clicking a button. The creator account doesn't have the option to remove the theme, even though the creator is the person who uploaded it. To take a theme off the Theme Garden, you must speak to an employee at Tumblr who has access to the Theme Garden and can remove your files.
To contact Tumblr, log in to your email account and compose a new email to email@example.com. Include your Tumblr account name, the name and number of the theme you want removed and a reason for its removal. Sign it and send it. If you don't hear from Tumblr in a month, follow up on the email with a second email that includes a copy of the first one as an attachment so that they can see how you submitted the request previously.
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