This feature predates the so-called "big-tree" on Geni. This tree presently has over 50 million profiles ( http://www.geni.com/worldfamilytree ), about half of the total profiles! With the very rapid growth of this tree that feature became rather useless. Because if you ARE in this tree then "everybody else" was half of Geni, and if you are not in the tree, as in your case, it means EVERYBODY else. So it no longer became useful as a filter.
I understand the concern with the "big-tree". However, as you said, evrybody is not in that tree. When I am searching for new family member with the same surname, I have to go through many pages where most of the profiles are from my tree. At least, I should be able to order these profiles using the column "administrator" in order to see all profiles "not administrated by me" and thus incuding the ones "not connected to me" together.
It always takes a lot of time to check which profile is new and potentially a new family member.
My family name is maybe rare compared to some others. However, my family tree contains around (only?) 300 people. There are around 100 more that are not yet connected to me, on Geni. Lokking at other sources, I can find also 200-300 others, in Brazil, Argentina, Porto Rico, USA, Asia, ... maybe coming from the roots .. or not.
When I get frustrated with GENI's search function, (which I find is often - since the search ability for non-pro members has been so crippled) - I just search GENI via Google. If you specify in the Google search to not provide results where your own name appears, then at least it filters out the profiles you are the manager for.
Hervé, have you looked at the new Surname feature that lists all public profiles with a particular surname ( http://www.geni.com/surnames/panetto ). Lists 147 public Panetto profiles. From there, you might be able to look at managers or those trees for common roots.
Maybe it is possible to add here http://www.geni.com/worldfamilytree also counter of (Claimed) Geni users?