There were many ways how these successions worked in different countries.
To summarize the well written source in Wikipedia, giving the key words:
One was Primogeniture
Where all goes to the firstborn, this was usually working with male successors, but for example in Basque culture they always preferred the firstborn without gender preference. Semi-Salic agnatic-cognatic hereby means if all the male successors died, in succession women came in the similar order to men. Some form of Primogeniture was widespread in Western-European kingdoms.
Secondly there is Agnatic Seniority
A principle where the oldest patrilinear successor takes the titles. This method used by for example Kievian Rus, Kingdom of Poland, and in the present day by the Saud house.
For the third there Elective Monarchies
The monarch's person was elected by and from the rightful electors. Best example was the Holy Roman Empire.
Ultimately what you are curious of mostly the Gavelkind
In some regulations there was a compulsory share of the titles between the successors. So the most important titles left for the first successor, and the rest was divided between the immediate successors. Of course not all of them since the succession list could be huge with bigger families.
Adding few comments: there were various local uses of these principles, other - less spread - methods, and the succession often meant of the main title (Grand Duchies, Kingdoms, Empires), often occured that brothers received lesser titles by grants to cool them down, especially if the successor was young and healthy since in that case their succession would be hopelessly far in time.