As with many other files, you have worked with in this book, core.css and the other style sheets lives in the 12 hive on each Web server; therefore, if you modify and save them with SharePoint Designer, you will create customized pages. Child sites do not inherit from a customized core.css; they will still point to the un-customized page in the 12 hive. If you repeat this on a number of sites, each site will have its own copy of core.css. Then if the core.css in the 12 hive is changed and distributed to the Web server(s), those changes will not affect your sites.
For more information about the 12 hive, see, Chapter 1.
When you need all sites in a site collection to have the same branding, then ...
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