By default each site in the multisite will act in the same way as a stand alone site – completely independent. There are a number of plugins that will allow for a global network search though.

I may try theĀ Multisite Global Search plugin… once I get permissions to Create Views with my PHPMyAdmin user!

Another option that UMW used was Google’s Custom Search Engine (CSE) – this may give more control than the default WordPress search.