The Government of Ireland Act, also known as the Fourth Home Rule Act was intended to provide a solution to the problem that had bedevilled Irish politics since the 1880s, namely the conflicting demands of Irish unionists and Irish nationalists. Nationalists demanded a form of Home Rule, believing that Ireland was poorly served by the British Government in Westminster and its Irish executive in Dublin Castle. Unionists feared that a nationalist government in Dublin would discriminate against protestants and would impose tariffs that would unduly hit the six North Eastern counties of Ireland, which were not only predominantly protestant but also the only industrial area on an island whose economy was largely rural and agricultural. Extremists in both camps threatened violence if their will was not upheld. Partition, which was introduced in the Government of Ireland Act, was intended as a temporary solution to the problem, allowing Northern Ireland and Southern Ireland to be separately governed as regions of the United Kingdom of Great Britain and Ireland. Ironically, one of those most opposed to this partition settlement was the leader of Irish unionism, Dublin-born Edward Carson, who felt that it was wrong to divide Ireland in two.
In reality, however, while Northern Ireland did become a functioning state, with a parliament and executive that existed until it was suspended in 1972, Southern Ireland never became a functioning reality. An Irish Republic had been proclaimed by the illegal Dáil Éireann, or 'Assembly of Ireland (Parliament), formed by Sinn Féin MPs elected from Ireland in the United Kingdom general election in 1918. The first general election to the House of Commons of Southern Ireland in 1921 was used by Sinn Féin to produce a new Dáil, the Second Dáil. Sinn Féin won 124 of the 128 seats, all without a contest. (Four were won by Irish unionists.) When the new Parliament of Southern Ireland was called into session in June 1921, only the 4 unionist members of the House of Commons of Southern Ireland, and a handful of appointed senators, turned up in the Royal College of Science in Dublin, where the meeting was scheduled to take place. As a result, Southern Ireland never formally came into being.
It did however play one technical role in January 1922. According to British constitutional theory, Dáil Éireann had no legal or constitutional existence. The valid Irish parliament remained the House of Commons of Southern Ireland, created by the King-in-Parliament. But according to Irish republican theory, the Dáil was the legitimate parliament of the Irish Republic. As a result the Anglo-Irish Treaty, signed by representatives of the British and Irish Republican governments in 1921, was submitted to both assemblies, even though they actually consisted of the same membership (bar the four unionist members of the House of Commons of Southern Ireland who refused to sit in Dáil Éireann). In December 1921, the Dáil formally but narrowly ratified the Anglo-Irish Treaty, giving it validity in the eyes of the majority of TDs and of the electorate of Ireland. (The President of the Republic, Eamon de Valera, resigned in protest.) In January 1922, the House of Commons of Southern Ireland formally met to ratify the Anglo-Irish Treaty, giving it validity in British legal theory. (Anti-treaty TDs stayed away from the meeting of the House of Commons of Southern Ireland, meaning that its passage was a formality!).
Both rival parliaments each then produced their own interim administrations. Michael Collins became Chairman of the Provisional Government; his installation symbolised the differing political procedures being followed. According to British constitutional theory, he met the Lord Lieutenant, Viscount Fitzalan, to be formally installed as the Crown's prime minister. According to Irish theory, he met Fitzalan to accept the surrender of Dublin Castle!. Arthur Griffith became President of Dáil Éireann (reverting to the earlier title, in preference to de Valera's loftier President of the Republic). Both Dáil Éireann and the House of Commons of Southern Ireland were then replaced in a shared new election, which produced a body variously described as the 'Third Dáil', the 'Provisional Parliament' or the 'Constituent Assembly'. With the assassination of Collins and the death a week earlier of Griffith, both in August 1922, their offices came to be held by one man, W.T. Cosgrave, who in effect merged both systems of government into one interim system, pending the coming into force of the 1922 Constitution of the Irish Free State in December 1922. (The scale of the constitutional complexity was shown when Dáil Éireann, which was still technically the parliament of the Irish Republic, accepted a message sent by the Lord Lieutenant, the King's representative. By the end of 1922, almost everybody was confused as to the precise status of the parliament meeting in Leinster House, and as to whether it was the parliament of the Irish Republic or the parliament of Southern Ireland, both simultaneously, or either at different times!)
In summary, in strict British legal terms, the state of Southern Ireland was the entity created by the Government of Ireland Act, 1920 which was meant like its sister creation, Northern Ireland, to have responsibility for the governance of Ireland from 1921 on. However in reality, it was only a state on paper. It was overshadowed by the Irish Republic, which existed from 1919 to 1922 and which had popular support, and the new Irish Free State which in both Irish and British constitutional theory replaced both the Irish Republic and Southern Ireland in December 1922.