I use quit some time to search a person in my tree, is there a function for?
The FamilySearch is a shared worldwide tree. It does not have individual trees. To find people in the shared tree click on Search and them Family tree. There is a Recents list of the last 50 records you viewed. (Image from the New Home page)
You can also "follow" up to 4000 profiles. From your Following list, you can search by name.
the average person who traces most lines back 10 genrations or more - has literally millions of people they could be related to in one way or another. All of that could be intrepreted as "my family tree:"
as other state this is not a system where people have private family trees that have a resonably low number of entries. This is a collaborative tree wit literally billions of people all connected together.
The FOLLOW feature though is a nice feature to keep track of the people you want to keep tabs on.