Final answer:
Depending on the historical period, the successor of a childless German king was typically chosen by electors (during the Holy Roman Empire), or emerged from the nearest relative in the royal lineage, guided by political alliances and familial ties.
Step-by-step explanation:
When a German king died childless, the process of determining his successor depended on the historical period in question. During the era of the Holy Roman Empire, a new emperor was not determined by direct hereditary succession. Instead, after the implementation of the Golden Bull in 1356, several key electors, specifically seven princes known as electors, were responsible for selecting the Holy Roman Emperor.
The rise of constitutional monarchy in Germany, with the German Empire's establishment at Versailles following the Prussian victory, did not fundamentally change this process. Instead, the empire functioned as a constitutional monarchy within which an emperor (Kaiser), typically hereditary within a royal family, held significant power, but other factors such as political alliances and familial ties across Europe also influenced succession.
In instances of childless monarchs, the throne often passed to the nearest viable relative, which could include nephews or cousins, as was the case with Emperor Franz Josef of Austria-Hungary, whose nephew Franz Ferdinand was set to inherit the empire. This practice also resonated in England, where Elizabeth I's nearest living male relative, her first cousin James VI of Scotland, took the throne as James I, operating under the belief in the 'divine right of kings.' The successors of childless rulers were typically those who could claim some blood relation and were often agreed upon by the ruling classes to preserve the stability of the empire.