suddently think of this today, by using the meta index nofollow, this can prevent the bot from crawling to external site, and thus preventing links to unrelevant site, and to bad neighbourhood as well. is there any proof that this helps page ranking?
It depends, if the meta nofollow is about all links on that page, it will not help your site because then the links you have from that page to other pages on your site will not be counted either. As for linking to bad neighbourhoods: if you have to, use rel no follow.
It will not help your page ranking, maybe harm your page rank. To prevent link to bad neighbourhoods, it's good. Prevent link to unrelevant sites, it's a harm to you. Though links to unrelated pages will not place the same weight as links to similar pages, they do help your page rank. Statcounter has 90% of its backlinks to unrelated websites, but its PR is 10.
"rel no-follow" might give credits on other aspect but not help SERPs. Google does not count these links as backlinks
Well, their rankings can hardly get better than they already are, can they? Sure, PR can go up, but their PR is likely to go up anyhow, from new links.
There are two different nofollow tags with the same name but different meanings. <meta name="robots" content="nofollow"> -- controls spiders <a href="http://site.com/" rel="nofollow">link</a> -- don't pass PageRank HTML: The nofollow meta tag in the page header has no effect on PageRank, as PageRank is still passed to all external pages (if they are already indexed). The only way to stop PageRank being passed on to another site is with the rel="nofollow" attribute on the link itself. Passing PageRank to other sites does not reduce the PageRank of your own site. PageRank Leak is a myth! Cryo.