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It seems undisputed that by including the keyword in the link text on site A, B, and C, you will help the ranking for that keyword on both the site linking from and the site linking to, correct?
What about linking from the main multi-topic site back to the affiliate site also including the keyword in the link text. It seems to me this would improve the rankings for the respective keyword on the affiliate sites, yet while diluting the 'voting power' of any other links on the same page of the main site or below - in otherwords your leaking some of your link voting power to the affiliate sites in attempts to boost their rankings for certain keywords.
Or is it best to have a few outbound links and not link back to affiliate site?
The other strategy would be to have a circular link pattern in which Site A has a link to not only the main site but also to Site B using topic B in the link text. Site B has a link to site C with topic C in the link text. Site C has a link to Site A with topic A in the link text. While this leaks some of the voting power from the affiliate sites, wouldn't it boost their rankings for their respective topics?
Or is the bottom line to have as few outbound links as possible on the affiliate site and just link one-way to the main site?