Are your Samsung Galaxy S3 already upgraded to the latest ICS software update? Well, I guess that your wondering why quick search function on home screen search bar was totally removed. Usually, you can use it to look up anything on the phone like, names, contacts, apps, etc. This was intentionally removed by Samsung because Apple has filed an injunction against Samsung for the Universal Search function saying the feature infringes on Apple’s patents. Samsung taken the safe way out and totally wipe the Universal Search from the Galaxy S3.
Now if you want to restore it back without Samsung's aide, you can simply fix it by installing the GoogleQuickSearchBox.apk file on Galaxy S3.
1. Download and install ES File Explorer File Manager from Google Play store. You can also download any other file explorer that enable root access on rooted device.
2. Allow root access for ES File Explorer File Manager to complete the job. To do so, first press menu button and then tap on Settings. Locate and tick on Up to Root first and then tick on Root Explorer. A pop up massage ask you to grant the access, tap on Allow/Grant button to allow root access. Now, tick the Mount File System Option. Once all three option is ticked the way we mentioned above, you are ready to exit from Settings option.
3. Locate the GoogleQuickSearchBox.apk file in phone SD card that you copied earlier. Now long press on it and tap on Copy then. Press the Up button located at top until you reach the root of the device (you will see / at the top).
4. Reach /system/app folder and then paste GoogleQuickSearchBox.apk by tapping on Paste button located at top.
After that, long press on the copied file (i.e. GoogleQuickSearchBox.apk) and then tap on Properties option. Next, tap on Change button located under Permission section. Now, tick the Read box in front of both Group and Other [set permission to rw-r--r--]. Now tap on OK button to enable new permission setting. Quit ES Explorer now.
5. Go to Settings > Application Manager > All and clear data/cache for Google Search and Google Services Framework by tapping on the function name and then clear data/cache related button.
6.Reboot your Galaxy S3
Source: Android central.