Google_Maps_iPhone.jpgMediaPost has a report on how Google, having conquered desktop search, increasingly appears to be “extending its dominion” to the mobile Internet:

“With a 62% share of mobile Web searches, Google’s market share on cell phones is roughly on par with its commanding lead in PC-based queries. Helping foster that connection, Google recently redesigned its mobile site to more closely resemble the desktop version.”

The report also said that Google is leading in SMS-text searches, with a 40% share compared to Yahoo’s 27%, according to Nielsen Mobile. That’s interesting, since text searches have a slight lead in popularity over mobile Internet searches in the U.S. at present—probably because many more people either are familiar with SMS text messaging, or have phones or plans that can only do that and not access the mobile Web (at least without incurring higher charges).

“While Yahoo got into mobile quickly and broadly and continues to lead as a brand in the mobile Internet, Google is positioning itself well as the leader in mobile search, through all forms including SMS, 411 and WAP (wireless application protocol),” said Nic Covey, director of insights for Nielsen Mobile, in the report.