The statement that the Mughal administrative system was a 'centralised despotism' largely holds true, reflecting the absolute authority of the Emperor and the hierarchical structure of governance. At its core, the Mughal system was designed to concentrate power in the hands of the monarch, who was considered the ultimate source of all authority, often claiming divine sanction for his rule.

Centralised Aspects:

1. Emperor's Absolute Authority: The Emperor was the supreme head of the executive, judiciary, and military. His word was law, and there were no institutional checks on his power. All major appointments, policy decisions, and judicial pronouncements emanated from him.
2. Hierarchical Bureaucracy: A vast and elaborate bureaucracy, comprising various departments and officials (like the Diwan for finance, Mir Bakhshi for military, Mir Saman for imperial household, and Sadr-us-Sudur for religious affairs), was directly accountable to the Emperor. These officials, known as Mansabdars, held ranks based on their military and civil responsibilities and were frequently transferred to prevent them from developing local power bases.
3. Uniform Revenue System: The land revenue system (Zabt, Dahsala) was centrally administered, ensuring a consistent flow of revenue to the imperial treasury. This system, though implemented locally, was designed and overseen by the central administration.
4. Military Control: The Emperor commanded a powerful standing army, and all military commanders (Mansabdars) were directly appointed by and loyal to him, ensuring military centralization.
5. Judicial System: The Emperor was the highest court of appeal, and justice was administered through a hierarchy of Qazis, with the ultimate authority resting with the Emperor.

Despotic Aspects:

1. Lack of Constitutional Checks: There was no written constitution or independent judiciary that could challenge the Emperor's decisions. His will was paramount.
2. Arbitrary Power: While Mughal emperors often strived for justice and good governance, their rule was ultimately based on their personal discretion. Punishments could be severe, and property could be confiscated at will.
3. No Hereditary Nobility: Unlike European feudal systems, the Mughal nobility (Mansabdars) did not hold hereditary rights to land or office. Their positions were dependent on the Emperor's favor, preventing the emergence of a powerful, independent aristocracy that could challenge central authority.

Nuances and Limitations:

Despite this strong centralisation, the vastness of the empire and the limitations of communication and transport meant that complete, absolute control was often a theoretical ideal rather than a practical reality. Local intermediaries (like Zamindars) played a significant role in revenue collection and local administration, often enjoying considerable autonomy as long as they paid their dues and maintained order. The Emperor also relied on a network of spies and informants to keep abreast of provincial affairs. Furthermore, the need to maintain the loyalty of diverse religious and ethnic groups often compelled emperors to adopt pragmatic and inclusive policies, tempering the purely despotic nature of their rule.

Conclusion:

The Mughal administrative system was indeed a highly centralised despotism, with the Emperor at its undisputed apex. The elaborate bureaucratic and military structures were designed to ensure his absolute authority and the efficient extraction of resources. While practical challenges and the need for local cooperation introduced some elements of decentralisation, the fundamental character of the state remained one where power was concentrated and exercised largely at the Emperor's discretion, making the description of 'centralised despotism' largely accurate.