What happens following King Lear's abdication?

Evidently Shakespeare thought that an absolute monarch was necessary for a stable government. When Lear decides to abdicate and divides his kingdom into two parts, he not only brings down disaster on his own head, but he creates chaos. This is represented by conflicts between Edmund and Edgar, between Gloucester and Edgar, and later between Edmund and his father. There are conflicts between Gloucester and Regan, conflicts between Gloucester and Albany, and between Albany and one of his servants, into which Regan intervenes. The fact that one of Gloucester's servants turns against him suggests a revolutionary spirit developing at the lower social levels. There are also conflicts between Goneril and Gloucester and between Cornwall and Gloucester. Then Kent enters the scene, and there are conflicts between him and Oswald, between Kent and Albany, Kent and Regan, Kent and Goneril, and Kent and Cornwall. Lear has serious conflicts with both his daughters and their husbands. Then Lear has a conflict with the storm, which seems to symbolize the coming troubles that will beset the land. Edgar has a similar sort of conflict with the elements. After Cornwall's death, there is conflict between Goneril and Regan over the handsome, ambitious Edmund. There was already a conflict brewing between the sisters' husbands over political and territorial matters, as Gloucester confides to Edmund. When news of Lear's mistreatment by his two daughters reaches France, a French army invades England, leading to a large-scale international conflict. Cordelia, who arrives with the French forces, is now in conflict with Goneril, Regan, and Albany. Edgar comes into conflict with Oswald and kills him. There are so many conflicts going on in different places at more or less the same time that it is hard to keep track of them all. This may have been Shakespeare's intention. He may have wanted to represent a state of general chaos. None of these conflicts would have occurred if Lear had not given up his throne and with it his status as a symbol of law and order.
When Macbeth murders the legitimate King Duncan, a state of chaos develops in Scotland, leading to the invasion by an English army of 10,000 men. The monarch must be powerful and legitimate.
Shakespeare dramatizes a similar theme in Julius Caesar. After Caesar's assassination, a power vacuum is created. He was a symbol of unity, stability, and supreme authority, and he was on his way to becoming crowned king when the conspirators struck. Mark Antony predicts what is going to happen as a result of absolute rule being demolished.
Over thy wounds now do I prophesy
Which like dumb mouths do ope their ruby lips
To beg the voice and utterance of my tongue,
A curse shall light upon the limbs of men;
Domestic fury and fierce civil strife
Shall cumber all the parts of Italy;
Blood and destruction shall be so in use,
And dreadful objects so familiar,
That mothers shall but smile when they behold
Their infants quarter'd with the hands of war;
All pity choked with custom of fell deeds,
And Caesar's spirit ranging for revenge,
With Ate by his side come hot from hell,
Shall in these confines with a monarch's voice
Cry “Havoc!” and let slip the dogs of war,
That this foul deed shall smell above the earth
With carrion men, groaning for burial.
Act III, Scene 1