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I would aim for variety in your linking domains, which usually means 1 link on 1 site. But bear in mind a large part of link-building is building relationships, so you shouldn't necessarily 'never talk to them again'. I would aim to build a link on a site via quality content, which you then go out of your way to promote via social media, etc. as well as ensuring you reply to any comments and stay involved in the conversation. Not only does this make your link more valuable, but helps you build stronger relationships. I'd also stay away from using direct match anchor text on your keyword targets - use your brand name to link back and you'll increase your overall domain authority, which will help you rank (assuming your on-site elements are solid). But back to the question, generally speaking I'd always aim for 1 link on 5 sites vs. 5 links on 1 site, just make sure those sites are relevant, high quality and not involved in any potentially worrying activities (such as selling links, aggressive advert blocks, etc. etc)

I'd try SEMRush - http://www.semrush.com - although they only offer some of the data for free, I'd check it out - sounds like it can help you and would serve as a good comparison to Ahrefs.