There is a castle in Switzerland that no longer belongs to the family who built it. Habsburg Castle, raised in the 1020s by a count named Radbot of Klettgau, was lost to the Swiss Confederacy in 1415. By then, the dynasty it had named was ruling half of Europe and had long since stopped needing it.

The Habsburgs spent two centuries as minor counts in the borderlands of what is now Switzerland and southern Germany, accumulating land through marriage and the convenient extinction of neighbouring noble families. The pivot came in 1273, when Rudolph, a seventh-generation descendant of Radbot, was elected King of the Romans as a compromise candidate no one expected to last.

Rudolph lasted. He defeated and killed the Bohemian king Ottokar the Second at the Battle of Marchfeld in 1278, seized the dead king's lands, and appointed his own sons as Dukes of Austria. The family moved its base to Vienna. That shift was everything: the Habsburgs were no longer Swiss counts but the lords of the eastern Alpine duchies, with the Holy Roman Empire within reach.

The imperial throne became theirs in 1440 and they held it, with rare interruptions, for nearly four centuries. The high tide came under Charles the Fifth, elected Holy Roman Emperor in 1519. Through his parents' marriage he already held Spain, its American colonies, southern Italy, and the Habsburg Netherlands. His realm was the largest in European history to that point, and he was the last emperor to be crowned by a pope, at Bologna in 1530.

Charles abdicated in 1556 and split the inheritance: his brother Ferdinand took Austria and the imperial title; his son Philip took Spain, its empire, and the Low Countries. The dynasty now ran in two parallel lines, intermarrying so relentlessly that the inbreeding wrote itself onto their faces. The protruding lower jaw known as the Habsburg jaw, the heavy lip, the arched nose: these were not merely portraits. They were the cost of consolidation.

The Spanish line paid the final price. Charles the Second of Spain, the last of that branch, was so severely disabled by generations of close marriage that contemporaries called him the Bewitched. He died in 1700 without an heir. The War of the Spanish Succession followed, and the Bourbon dynasty took Madrid. The Spanish Habsburgs were gone.

The Austrian line survived a little longer. Maria Theresa, the dynasty's most formidable ruler of the eighteenth century, defended her inheritance against all challengers after the male line died out in 1740. She married Francis Stephen of Lorraine, and the dynasty continued as the House of Habsburg-Lorraine. Her son Joseph the Second would sit on the imperial throne after her.

Napoleon ended what remained. On 6 August 1806, the last Holy Roman Emperor, Francis the First of Austria, dissolved the empire under pressure from Napoleon's reorganisation of Germany. The institution the Habsburgs had dominated for nearly four centuries simply ceased to exist. Francis kept the title Emperor of Austria, a new crown he had invented for himself two years earlier in anticipation of the loss.

The dynasty limped into the twentieth century. The First World War destroyed what was left. On 11 November 1918, the last Habsburg ruler, Charles the First of Austria, issued a proclamation renouncing any role in state affairs. He did not formally abdicate. It made no difference. Austria and Hungary both abolished the monarchy, and Charles died in exile in 1922.

The family that had once held Spain, Mexico, Bohemia, Hungary, and the Holy Roman Empire was reduced to private citizens by parliamentary vote. What survived was not power but the name: a castle in Switzerland, a crypt beneath a Viennese church holding a hundred and fifty of their dead, and the unanswerable question of whether so vast an empire collapsed because the Habsburgs held too much, or because they tried to keep it all in the family.

Otto von Habsburg, Charles's eldest son, did not formally renounce all claims to the throne until 1961. The hawk's hill had taken a very long time to let go.