Oh, they sure do. Just a few years back the company behind mapy.cz had a majority share in search in Czech Republic. Somewhat of a rarity in Europe, maybe even (latin writing) world. Google ads were everywhere - radio, tv, billboards, etc... not to mention online.
Well, I'm sure Google Inc would love to dominate but I believe their fall from grace is evidence Google engineers don't want to. Or maybe I'm off base. Nobody dominates forever.
