Sorry, Cesar - you're right, this thread went way off course.
My notes on 301 as preferred vs rel=canonical were strictly focused on potential "duplication issues" brought up by Federico as related to Desktop URLs. The 301, you're right, is the wrong tool for the job when it comes to Desktop/Mobile.
The page I linked to originally - here: https://developers.google.com/webmasters/smartphone-sites/details#separateurls - has the instructions you'd want to follow under "separate URLs."
To clarify with Google which page should be served to which search users (Desktop vs Mobile), you need 1) a rel=alternate tag pointing from Desktop to Mobile and 2) a rel=canonical tag pointing from Mobile to Desktop.
Effectively if you will have the same canonical for both versions - the Desktop home page. Whether or not you have rel=canonicaled the Desktop back to itself (again this doesn't accomplish much but it won't hurt you), the Mobile home page (following the instructions from Google) will be rel=canonicaled back to the Desktop home page.
And yes, if your Mobile home page has a lot of links pointing to it, using this setup should increase the overall authority and ability to rank of your Desktop home page. It will consolidate that link equity at the Desktop home page URL.
Both pages will remain indexed, but Google (learning from the rel=alternate tag) will serve up the Mobile home page only for mobile search users.
Hope that clarifies a bit. Disregard the discussion between Federico and I on the correct use of 301s in this thread, as it was off topic. In short, a 301 will not serve you well in this case. You want one of the three implementations recommended by Google on the page I linked to above (and in your case, the third option for separate URLs sounds best to me).
Best,
Mike