"To complete the search" means to finish looking for or examining something thoroughly, until all relevant information or items have been found or explored. Full definition
After completing the search will show many singles appear on the screen, breaks by page numbers. (adultfindout.com)
The National Sex Offender Registry (NSOR) service completes a search of a national database of sexual offender records from all 50 states, the District of Columbia and Puerto Rico (including registered sex offenders). (orangetreescreening.com)
You might want to tag those right away with the competitor's name; you can do it when Rank Tracker completes the search in the Add tags field, before you click Finish. (link-assistant.com)