How much link juice does the root domain/homepage pass internally to the sites inner pages?

Its more dependent on navigation structure. So if you have a PR6 page and you but five pages in the top navigation menu in most cases you will see those pages become PR5 or P4s (back when we could relatively trust Toolbar PR)

I know one of the old mantras is the Google ranks pages not site but yes I have come to accept that Google also uses SITE authority as a factor.

PR is page level, there's no such thing as domain PR.

What your seeing is link sculpting whether the site owner meant for it to happen or not.

You can take any page on your site & build it up as the strongest authority page for the entire domain, it doesn't have to be the Index page.

I have internal pages with higher PR than the Index page on the same domain, happened long before public PR stopped updating.

It passes quite a lot actually, assuming the site has a good internal linking structure as Mike said.

There are a lot of factors in play other than just PR/PA/DA. There are a lot of trust metrics and other secret sauce stuff you are never going to know about.

Essentially though, if you can build up a high quality site, with some good links, flow the juice around by interlinking well, you will be set.

I am pretty sure that links from within the body content of say a page on your site, are given more weight internally than links from the nav bar/sidebar. So that is something to consider also. Interlinking to your internal pages Wikipedia style is a really good practice that not enough webmasters do.

This is my understanding from my own experience and I do not wish to try and "prove" this to anyone.

"link juice" flows out most powerfully to the top, left links on the page and diminishes towards the bottom links, but depending how many links there are on the page, it may not pass any "link juice" out through the bottom links at all by the time it gets there. Googles reasoning is that if the webpage is built for users, the top links would be the most important, and rightfully so.

In your average website where every page on the website, that may have some PR of it's own, points back to the main page of the website, normally that will be the most "juice filled" page. The first link off that page is a powerful one.

Believe it or not, for instance on my homepage, where I point out to many pages, as my homepage links out to them, they also link back to me, so there is some "link Juice", with diminishing returns going back again also.

Pagerank is not rocket science, just think of each page like a cup that is filled by other cups, but each time you pour, a little juice gets spilled and lost of the floor.

Edit: I was rereading your question, link juice travels through the link structure, not the file structure. Pagerank is about links.

BTW zero backlinks I am sure would not be accurate, I could create a page on my website right now and link it off the homepage (backlink) and it would essentially be PR1 but the toolbar would show it N/A, because the real pagerank at google, updates very quickly, but the toolbar is hardly ever updated.