How did the Habsburg family gain control of Austria in the late 1200s?

The Habsburg family’s control of Austria began in the late 13th century following the rise of Rudolf I of the House of Habsburg.12

Before the Habsburgs, Otakar II of Bohemia had gained control of Austria and Styria during a period of political instability in Germany. After Rudolf I was elected German king in 1273, he moved to challenge Otakar’s powerful position. Rudolf placed Otakar under the ban of the empire and, supported by allies including the Hungarians, invaded Austria.341

Otakar was defeated in 1276 and subsequently killed at the Battle of Dürnkrut in 1278 while attempting to reclaim his lost territories. Following these victories, the duchies of Austria and Styria were declared vacant. In 1282, Rudolf I received permission from the German princes to grant these lands to his sons, Albert and Rudolf, establishing the territorial foundation of the Habsburg dynasty in the region.3412