We've changed our search box to search using our enterprise search center tool rather than just searching the site. The problem is that the search results page comes back from the enterprise search center. That page has a link home that takes people back to the search center, not the home page of the site.
Anybody know of a good guide on how to modify the search results page so that its banner and home link are consistent with the rest of the site?
OTB Enterprise Search Center uses mimimal.master page which does NOT have all elements that your custom(or other OTB ) master page has. You have to develop a custom master page for search center or use your existing master page and make sure that they are compatible with search center controls and web parts.
Following links should help you get started:
SharePoint 2010 Modifying the Search Centre Master Page and Page Layouts
Making SharePoint 2010 search pages work with a proper master page
