Most sites that gain links naturally get a mixture of links pointing to the home page and links pointing to internal links. If your site has all its links pointing to the home page then it would be a clue to the search engines that the links may not be natural.
Deep links help internal pages in your site rank. In addition, links to your internal pages also helps push up your home page and any page in your link structure above the internal page.
Also, deep links help you target specific content on your site, and specific search keywords relating to that content. You can use them to drill down to more tightly targeted content, keywords, and markets.
When it comes to improving "link popularity", it's better to avoid all back links pointing to your homepage specially if your site has varied content... Besides, deep links could also lead a site to gaining PR in its internal pages overtime
deep links will rise your both pages pr ( internal and of homepage) better to get deep links than of homepage
Deeep Links really matters. If your website is based on several topics and you can to optimize it separately with different keywords then you used deep links for optimization. It really effective way to convey your pages to others.