Expanded from an earlier answer

The idea that Prussia was an incubator of German illiberalism was one that was common during the war. This anti-Prussian position contended that institutions like the German General Staff, the traditions of aggressive war, and strong centralized leadership began in Prussia and infected the rest of the German body politic. Propagandistic educational films like Frank Capra's Here is Germany is only one example of this line of thought. Yet propaganda is different than policy. For example, the Soviets emerged postwar as one of the stronger advocates for abolition, but a lot of their wartime propaganda directed towards Germans emphasized the heroic role of Prussian resistance and disobedience in 1813 where commanders like Yorck disobeyed orders and sided with the Russians against Napoleon. So the abolition of the country was more than just the tale of trying to eliminate a problematic, allegedly innate, tradition in Germany.

Although the exact genesis of the abolition of Prussia is difficult to pin down, all three of the Allied leaders (FDR, Churchill, and Stalin) had assumed that postwar Germany was to be territoriality truncated and rearranged. Much of this built on a consensus that the peculiar features of German unification gave Prussia an outside importance over the German state and channeled Germans' spirits into aggression. Not only did this call for a permanent reversal of the Anschluß, but even a revision to pre-1871 borders.

As early as March 1943, FDR entertained visions of multiple postwar German states in conversation with British Foreign Secretary Eden in which Allied propaganda would encourage regional German disunion not only to undermine the immediate wartime situation, but also psychologically prepare Germans for a multi-part Germany. At Tehran, FDR floated the idea of a five-state Germany and neutralization of the Kiel Canal and the Saar/Ruhr area under international control. As typical for FDR, it is difficult to gauge how serious he was about these ideas, but anti-Prussian sentiment did figure into several quarters of American government. A State Department subcommittee on potential political problems in July 1943 produced a report essential that concluded that it was essential that "the political and military power of Germany be reduced and that the domination of Prussia over the rest of Germany be broken." Elsewhere, the US military and OSS commissioned reports on exactly what was the nature of "Prussian militarism" and how to remove it root and branch from the postwar order. In the public sphere, political scientists like the emigre Arnold Brecht and geographer Robert E. Dickenson argued in books and articles that not only was Prussian dismemberment desirable, but achievable.

For his part, Churchill too argued for a disestablishment of Prussia as an integral part of the postwar settlement. This was part of a wider plan to rearrange the map of Central Europe and ensure that Germany would not rearm. A May 1944 cable to FDR, the British Prime Minister noted:

At Tehran my suggestion for the isolation of Prussia was considered far too modest by you and [Stalin]. Everybody expects complete forcible disarmament of Germany, possibly extending to civil aviation, to be made. There are other very grave questions open. For instance, how are the Poles going to be compensated if they do not get East Prussia and certain territories up to the line of the Oder in return for the Curzon Line which the Russians will certainly demand?

One of Churchill and the Foreign Office's pet projects during the midwar period was to foster a Danubian federation that would unify southern Catholic Germany, including Austria, that meshed with existing British connections in Southeastern Europe, and would act as a counterbalance to the allegedly more militarist northern Protestant Germany. During the tumultuous EDC negotiations in the early 1950s, the aged Churchill would lament to his personal physician Lord Charles Moran that the current difficulties was that Germany was divided vertically, not horizontally as pushed for at Potsdam This horizontal division would have contained a truncated Prussia, according to Moran's reminiscences, that would have contained the state and preserved it as a local counterweight.

Stalin characteristically played his cards close to his chest, and a number of the ministerial archives on his diplomacy regarding the German question remain closed, making it hard to come up with his firm opinion. But dissolution of Prussia as a state entity did suit the larger Soviet agenda for expansion towards the Curzon line and Königsberg. As the Churchill cable indicated, postwar Poland would need to be compensated with Prussian territory to sate these demands. Abolishing the Prussian state by the Allied powers removed a legal obstacle to this Polish compensation. Thus it became in Stalin's interests to eliminate Prussia as an entity.

The Tehran Conference affirmed a loose commitment to a wider program of dismemberment, neutralization, and some dissolution f postwar Germany, but in a process that would become all too common, the Big Three disagreed over the specific details and punted a final arrangement further down the line. FDR told Hull in October 1944 that "I dislike making plans for a country which we do not yet occupy," a statement that not only exemplifies FDR's sometimes inconstant policy habits, but also the skepticism in some quarters over commitment to ambitious plans. This procrastination helped throw cold water on various schemes to radically redraw the map of Central Europe like the Morgenthau Plan.

In the US, various internal studies produced by emigres and other specialists revealed that radical restructuring might not be so practical after all. An OSS study produced by Marcuse and Felix Gilbert concluded that the Nazi state had defanged the Prussian Junkers in the former's drive for power, and that Prussia "is no longer the core of Germany." Other military studies on mass psychology emphasized that fear of a Carthaginian peace would stimulate revanchism. While there was a considerable vein of pop history on the "German problem" that filled Allied bookshelves, a good many German emigres and other specialists in Germany noted that "Prussia" was largely irrelevant to the Nazis, who originated in Bavaria, and the increasingly Germanized General Staff. There was much merit to these specialists' assertions. Prussia's influence on German affairs during the Weimar collapse was not part of a historical tradition of illiberalism, indeed, quite the opposite. Prussia was one of the electoral bedrocks for the parties of the Weimar coalitions. While there was a somewhat authoritarian character in Prussia's Land politics, the state was one of the obstacles for authoritarian politics in Weimar. It was only when the Chancellery started stripping Prussia of its federal independence in the 1930s that the largest German Land emerged as a tool for illiberalism.

Hypothetical restructuring of Germany soon became a possible reality as the Allies assumed control over Germany. The emerging Cold War drew attention to the need to restore Germany on a functional basis by both superpower blocs. The tendency to punt details of a solution to the German question during the 1944 and 1945 conferences meant that in many ways the contours of German division were being determined by facts on the ground, not organized plans drawn up in foreign offices. Although France, a relative late-comer to the German question, kept alive ideas of partition, by 1946, it was clear that some sort of German state(s) was in the offing.

The formal abolition of Prussia by the Allied Control Council Law No. 46 in February 1947 emerged as an appendix to the stalled plans for a radical restructuring of Central Europe. Agreement to abolish the polity was one of the few issues left in which there was concord at the subsequent Foreign Ministers Meeting in Moscow between March-April 1947, and sanctioned Law No. 46, which was also one of the few agreements made at this conference. The abolition of Prussia also managed to gain two German collaborators. In the Western zones, the emergence of the southern German and Rhineland bloc under Adenauer's leadership had a longstanding antipathy towards Prussian political domination. Even though Adenauer's habits of rule would soon emerge to fit in the stereotype of Prussian authoritarianism, he always maintained a public aversion to Prussia, even when he advocated the necessity of a German unitary state. In the Soviet zone, the SED found itself more reluctantly supporting the abolition as it facilitated settlement of the Oder-Neisse, which the Soviet military government favored. The SED press in the run up to Law No. 46 carried several front page articles on the baleful legacy of Prussian militarism and how the only ones to mourn the loss of the state were class enemies like the Prussian Junkers and militarists. On the ground, SED activists were less enthusiastic about toeing the Soviet line over the Oder-Neisse and accepting the abolition of Prussia reinforced the permanency of this division. But a number of the SED leaders argued to their constituents that accepting these proposals immediately opened the door to a later territorial revision.