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I've been asked to register a domain that looks like it would belong to the big one (not a mis-spelling, they're a houshold name), and use it in an html mailshot to get people to click. They would end up at the smaller company's site via a redirect from that domain.
I think its a really bad idea, and unprofessional. Particularly since the large company has recently taken on the smaller one as a partner and this is considered big news for the small company. I can't see the large company being too happy about it if it happens and they find out.