Yes, it gets propogated to subdomains, but the point was that if you have subdomain X.y.z, as long as you set the cookie for y.z, the cookie is valid for X.y.z and U.y.z.

My point was that you don't want the cookie to be sent to other subdomains, so you'd actually want to set the domain to X.y.z. You can't do that if you're web domain is y.z.