> Surely it's the provider of the hosting who gets blacklisted not the > 'name' of the host.
RBL public black list companies keep a database of both IP's and domain names. While banning the IP does blacklist the hosting provider, banning the domain name follows them no matter where they host. Spammers know this which is why they purchase disposable domain names in bulk. I've seen a lot of disposable .co domains being used for spam lately.
