He did not exactly directly announced that a certain person will be heir to his throne. However, after he blesses and acknowledged the bravery of Macbeth and Banquo, he announces that his son Malcolm is now Prince of Cumberland, which only means that he can be the next king. Read act 1 scene 4.
In Macbeth? King Duncan names his son Malcolm The Prince of Cumberland who is the heir apparent. After his murder, Malcolm flees so Macbeth is named to be King but later on in the play Malcolm, Duncan's son, becomes king.
The three witches in the beginning of the play told Macbeth that he will be King. And his own ambition pretty much lead him to kill Duncan. *Lady Macbeth also has an influence in the murder of Duncan*
Duncan announces that Malcolm is heir to the throne. This is crucial to the devlopment of the play because Macbeth's chances of becoming king are reduced.
The Prophecy says Macbeth will be king. Duncan is king. Macbeth cannot be king while Duncan is king. Duncan will not be king when he is dead. Therefore, make Duncan dead.
What happened to Malcolm is that he later comes back home.And he soon becomes King in place of his father who was killed by Macbeth in act 2....
In his aside, Macbeth reacts with shock and fear to the king's announcement that his son, Malcolm, will be heir to the throne. He reveals his inner thoughts about the possibility of murdering King Duncan to make the prophecy come true.
After Macbeth, Banquo, and King Duncan exchange warm greetings, King Duncan announce Malcom as the Prince of Cumberland.
Malcolm is made heir to the throne in Shakespeare's "Macbeth" primarily through the endorsement of King Duncan and the support of the noblemen of Scotland. After Duncan's murder, Malcolm flees to England to ensure his safety and to rally support against Macbeth. Upon his return, he is recognized as the rightful heir due to his royal lineage and the need to restore order to Scotland. This claim is solidified when he gathers an army to reclaim the throne and restore justice.
Duncan declares his son, Malcolm, to be Prince of Cumberland, which means that he is the heir to the throne. This proclamation tells the audience that in order for Macbeth to become King, not only does he have to murder Duncan but Malcolm too.
No. King Duncan was clueless. He admits it himself: "There's no art to find the mind's construction in the face; he was a gentleman in whom I built an absolute trust." He had no idea what was going on with Macbeth. Macbeth really expected to be named as Duncan's heir (he was after all a successful warrior unlike the feckless Malcolm) and was shocked and hurt when Duncan named Malcolm Prince of Cumberland. And then Duncan says "And now the party's at Macbeth's place!" He was, as I said, clueless.
Duncan's grooms.
The "black and deep desires" he is talking about is the temptation to hurry along Duncan's death so he can become king quicker. At this point because Duncan has nepotistically named his son as his favoured heir, and so it looks like Macbeth won't become king just by waiting for it. The temptation is to help the prophecy along.