A continuation of my previous comparison between the two services, Tumblr and Posterous. Both services offer domain mapping, meaning you may create an A record for your top level domain or a subdomain to point to their service, so you can access your blog at your custom domain.
As I've mentioned earlier, Tumblr handles domain mapping better, so that, let's discuss about my own specific example:
I have a domain name "hamili.net", a Tumblr blog at "deuts.tumblog.com", and a posterous blog at "deuts.posterous.com".
When I create an A record for host "@" to point to Tumblr's server (I don't want to discuss how to do that here, check out their FAQ or help page instead) while my "www" record points to "@" from my domain registrar's control panel, if you point your web browser to "www.hamili.net" or "deuts.tumblr.com" - the address properly redirects to simple "hamili.net" only (http://hamili.net).
Now, when I create an A record instead for "@" to point to Posterous' server with other settings same as above, if you point your browser to "www.hamili.net" or "deuts.posterous.com" - it stays there i.e., without redirection.
With the latter, this means that I have three websites that update accordingly whenever I post new items. One at "www.hamili.net", one at "deuts.posterous.com", and one at "hamili.net". As far as I am concerned, I have traffic for the same content going to three different sites. There's no consolidated home page.
Now as far as Google is concerned (and other search engines as well), this means the same - these are three different home pages. And I may get penalized by Google for maintaining triplicate (not just duplicate) contents and my authority with regards to my content suffers.