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Blog syndication is definitely an area where you should tread very carefully and the SEO benefit is likely to be minimal and possibly negative. If you use syndication purely as a means of increasing brand awareness for your client and a means to gain some referral traffic then it can be useful in that sense - but is it more useful than just writing a quality blog and retaining it your client's own site and then earning links, shares etc because the content is so good? Quality and unique content is what should rank and by syndicating the content it certainly becomes of less value in Google's and readers eyes, especially if they keep finding the content in many other areas. I would advise your client to keep the content for themselves unless the volume of referral traffic they receive is that great, in which case they should perhaps consider providing the content to other sites but not necessarily retaining it on their own blog. Alternatively, they could provide abridged versions of their own content to other sites and retain a lengthy authoritative version on their own blog. That said, if the content is that good then there's no reason it can't do more good for you client if they just retain it purely for themselves and market it effectively.