This is probably a pretty basic SEO question, I am wondering if the major search engines, Google, yahoo, etc count links to specific pages of your site to increase that page's SEO ranking or do they look at every link that goes to a page on your site (regardless of which specific page it is for), such as http://mydomain.com/content/article and http://mydomainname.com/content/article345, as simply a link to http://yourdomain.com ?
Every page on your site can have a different pagerank, or seo ranking, based on the links going to it. And yes, every search engine counts every link going to any page on your site. So if you have a link to each of those 3 URLs you mentioned, your domain will be listed as having 3 links. You can check out the links going to all the pages on your site with yahoo, using the query site: link:yourdomain.com, which may have a different count than link:www.yourdomain.com, but that's getting into canonical urls and duplicate content issues ...
It should be specific pages rather than a site in general. Otherwise the related content/niche/links theory go to hell
Every page is counted separately with the anchor text of the link. This helps the SEs to rank each page for specific keywords.