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If cross-domain tracking is implemented correctly, Google Analytics generates cookies only for the first domain accessed.
A basic test for cross-domain (and cross-subdomain) tracking is that the first domain that a visitor accesses generates Google Analytics cookies but that the domain or subdomain that is linked to does not.
A separate set of cookies would undermine the very principle of cross-domain tracking. If sitea.com and siteb.com are to be integrated in Google Analytics profiles, data such as visit count must be read from a single __utma cookie, source must be read from a single __utmz cookie, and sessions must be managed with a single __utmb cookie.
For more on implementing cross-domain and subdomain tracking, see Google Analytics developer help.
