The Target cookie behavior depends on whether it is a first-party cookie, a third-party cookie with a first-party cookie, or a third-party cookie alone.
The first-party cookie is stored in clientdomain.com, where clientdomain is your domain.
The third-party cookie is stored in clientcode.tt.omtrdc.net and the first-party cookie is stored in clientdomain.com, where clientdomain is your domain.
Mbox.js/At.js generates an mboxSession ID. The first location request returns HTTP response headers that attempt to set third-party cookies namedmboxSession and mboxPC and a redirect request is sent back.
If the browser accepts third-party cookies, the redirect request includes those cookies, and the offer is returned.
If the browser rejects third-party cookies, the redirect request does not include those cookies, and default content is displayed for all locations on the page.
Some Ad Blockers will block the first or third party cookie, unfortunately, Adobe Target has no control over third-party extensions.
For more information on First or Third Party Cookies please see the following Documentation