The original poster asked for (among others) Denmark and Norway, which I'll cover along with Sweden. I'll limit my answer to the later part of the medieval age, from ca 1200 and forward, this was when the rules of the Danish nobility were finalised (Sweden were later, and Norway never had much of a nobility).
Denmark has few examples: The later king Christopher II only became a duke when he was 31 years old. The son of Valdemar Atterdag, Christopher, had a dukedom (he died before he could ascend to the throne). During the Kalmar Union, the later kings John and Christian II were not made dukes before ascending, but John's brother Frederick was.
Norway has only one possible example from the period, Haakon Magnusson. He was indeed made a duke, when he was 14 years old.
For Sweden, the first duke was created in 1255, Magnus Birgerson, younger brother of king Valdemar, but he held no special land for this. Their father Briger jarl was not actually king, but was the de facto regent. Of his other sons, Eric was made a duke when Magnus took the throne from his brother, and Bengt instead went into the church, after this, all sons of kings where made Dukes with duchies at about 20 years of age, unless they had actually succeded to a throne. Magnus' two younger sons Eric and Valdemar were made Dukes. Their brother Birger became king when he was 10 years old, his son Magnus was styled "Duke of Sweden", without any land attached. Eric's son Magnus eventually became king (too young to have held a duchy), of his sons, Eric rebelled when he was 17 and took control of most of Sweden, and his brother Haakon became king of Norway at 15. After this, we have only Albrecht of Mecklemburg's son Eric, who was "lord of Gotland", before we reach the Kalmar union. (After it, the tradition was taken up again, with similar results of constant rebellions).
To summarise: In Denmark, the tradition existed, but was never strong and it was mostly discontinued before the end of the medieval period. In Norway, the only possible Duke was also made one. In Sweden, this was done as a rule, and resulted in rebellion.