I have a main site and plan on having dozens of slave sites running in sub-directories. Currently I am using K2 to create articles on the main site but I want that the slave sites can create their own unique K2 articles.

Right now when I create a slave site and create a new article, that article is reflected on the main site as well. How do I stop such K2 article sharing across sites?

If you have the K2 article present in both site, this probably mean that you have decided to share them between website.

The first thing to do is to verify that you have effectivelly shared the K2 content between the websites.
Go in the JMS tools and verify that the table for this website has effectivelly links to the other site.
If this is the case and that all the take of K2 are shared then what you want is to replace the sharing by a physical copy.

To do that, you need to remove (drop) the table.
This can be done by the uninstall of K2 in the slave site that contain the sharing.
When K2 is uninstalled, you can decide to re-install it and will perform a physical copy.

K2 does not provide partial sharing.
So it is not possible to partially share the K2 content depending on the website.
This share all its content or nothing.

For the partial sharing, see the "Article Sharing for JMS"
www.jms2win.com/en/joomla-multisite?page...67&category_id=1
that is based on the standard joomla articles.