From Vanessa Fox, an ex-Google employee:
Google is no longer treating subdomains (blog.widgets.com versus widgets.com) independently, instead attaching some association between them. The ranking algorithms have been tweaked so that pages from multiple subdomains have a much higher relevance bar to clear in order to be shown.
It’s not that the “two page limit” now means from any domain and its associated subdomains in total. It’s simply a bit harder than it used to be for multiple subdomains to rank in a set of 10 results. If multiple subdomains are highly relevant for a query, it’s still possible for all of them to rank well.
It's unclear what the "some association" part is -- but the parent and child domain like
b.example.com obviously have a relationship of some kind, far beyond what two websites named
example-b.com would have.
I don't think any Google penalties can go upstream to the parent, otherwise a lot of web hosting services would quickly find themselves delisted, by this (sensible, IMO) logic:
In this instance I’m talking about the exception given to protect free hosts from penalties, particularly those who give their users subdomains such as Hypermart, Xoom, Wordpress.com, Blogger, Tripod etc. This exemption can’t only cover the popular free hosts otherwise no new freehosts would ever stand a chance. As soon as they got a single spammy user their whole site could get banned and poof goes their legit business.
Likewise algorithmically it can’t cover all free hosts because then the big ones like Wordpress.com and Typepad would all be penalized. On a foresight this would also include profile based social sites such as Myspace and outbound linking social sites such as Delicious.
Therefore penalties can only go downstream to the child subdomains from the parent.
Primary domains can pass a penalty to subdomains. Subdomains can’t pass a penalty to a main domain unless the main domain holds a clear relation to the subdomain.
It's not entirely correct to say that
example.com are unrelated (as far as Google is concerned). But it does appear that only penalties, not bonuses, are ever transferred across.