Search engines are commonly used for online political information seeking across the globe, yet it is unclear to what extent political search predictions vary across countries and over time. We provide the first systematic analysis into the representation of European and national politicians as well as an event of high European salience (Brexit) in search engine autocompletions. Our dataset collection includes predictions in nine European countries on the basis of proxies for the geolocations for European party leaders, Spitzenkandidaten in the 2019 EP election, and cabinet members. We characterize the variation and volatility of the search engine predictions for the same politicians and issues across countries and over time. These data allow us to estimate to what extent online users search for similar attributes of European politicians, how much search suggestions spill over across European countries, and whether a common European public sphere in search engine suggestions exists for Europe's political elite and the issue of Brexit. Finally, we discuss the benefits and shortcomings of the method and possible future directions for studying the European public sphere in political online search.