When a Geni User searches for a person using the search box on the top right corner of the Geni interface their results will be divided into two tabs. The second tab, Search Outside Your Tree, contains search results from other Geni trees.
Now you have control over the search privacy for every node you add or have added to your Geni tree. You can set the privacy for all nodes you have added in your Search Privacy settings. There are settings for your profile, for deceased profiles you have added, and for living profiles you have added. For additional control, you can enable or disable search privacy for each individual profile you have added. On the Edit Profile page of any person you have added you will see a new Searchable by the public checkbox you can use to change their public search setting.