Here's the fun part: if I type in Hotmail.com into my browser, I'm redirected to a page titled 'Outlook' that's on a subdomain of Live.com (outlook.live.com)

But if I type in Live.com, I'm redirected to the same page that says 'Outlook' but is actually outlook.live.com

So Hotmail is Outlook but Outlook is Live.com but Live.com itself is Outlook

yeah, but I'm pretty sure that mess is all Outlook.com underneath. I use gmail but also have an outlook account under the new service.

The branding is Outlook.com, but I think it's still the old Hotmail/Live infrastructure underneath.

I mean that would make sense and I don't really care what's under it, the fact of the matter is it does have a unified brand these days.