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Which scenario would be better for keeping PR on the home page.
1: A home page with many backlinks that is a dead end for the PR. Basically this is a home page with zero links including external and internal.
2: A home page with one link to an internal page that links back to the home page.
Sorry if this is obvious to some of you. It is not obvious to me. My gut tells me that scenario #1 the dead end home page approach would be the best at retaining PR but I am often wrong. Thanks for your help.
inbound links -> home page (dead end)
inbound links -> home page -> outbound link
inbound links -> home page -> page B -> outbound link
These three scenarios will all give you exactly the same PR on your home page. Adding a second page will give you another page with almost as much PR as the home page, without reducing the PR of your home page.
Now if you have a link from page B back to your home page, it will send its PR back to the home page. In the end, your home page would end up with about 3.5 times as much PR if the damping factor is 0.15.
Of course, that is a stupid thing to do unless you are only doing it as a PR experiment.