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tl; dr The empire was a collection of semi-autonomous states that shared a long coastline protected by a Marathan Navy.
Most of the answers can be found in Wikipedia.
Chhattrapati Shahu, a grandson of Shivaji, was released by the Mughals after the death of Emperor Aurangzeb. Following a brief struggle with his aunt Tarabai, Shahu became ruler and appointed Balaji Vishwanath, and later, his descendants, as the peshwas or prime ministers of the empire.[6] Wikipedia
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Maratha power was fragmented among several discreet fragments.
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In a bid to effectively manage the large empire, he gave semi-autonomy to the strongest of the knights, which created a confederacy of Maratha states.
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The empire had its head in the Chhatrapati as de jure but the de facto governance was in the hands of the Peshwas after death of Shahu and with the death of Madhavrao - I, various chiefs played the role of the de facto rulers in their own regions.
The article goes on to discuss each of Shahu's successors.
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Peshwa's were prime ruler of Maratha Confederation.
Although they were 'prime minister' to Chattrapati (or King) ruling from Satara. However they were de-facto rulers. Prominent peshwa's were Balaji Vishwanath & Baji Rao I. Chattrapati gave most of administrative powers to Peshwa who use it to conquer most of India and allocated the new won territories to various Generals including Shinde (gwalior), Holkars (central India), Bhosale (Central and East part of India including Orissa) and Gaikwads (Gujrat).
By the treaties most were suppose to pay 'Nazar' or tribute to Peshwa along with taxes collected.
It should be noted that Office of Peshwa was created on non-hereditary basis but Balaji Vishwanath took advantage of Shahu Maharaj who had least interest in administration (he spent most of his youth under Aurangjeb as his prisoner). Baji Rao I captured Malwa, his son spread empire to Gujrat and also collected 25% tax from Deccan (ruled by Nawab of Hyderabad). Until this point empire was centrally controlled barring some dispute over Gujarat where fights between Dhabade and Peshwa over territory. After battle of Panipat (3rd battle) Marath empire got weak and Madhavrao Peshwa decided to give autonomy to Shinde, Bhosale, Holkar and Gaikwar.
Edit : Source : History of Maratha I, II & III - James Grant Duff
All three books are in public domain, published 1826