This is a very complex time and period. I spent a lot of time trying to figure out the same things regarding the Maratha (who, from looking at the evidence, had a Emperor dethroned by a Chief Minister who was then dethroned with the previous offices continuing but powerless). Mysore seems to be in a mostly similar position.
Maharaja of Mysore
In the beginning of the 18th century, Mysore was ruled by a maharaja. There were four maharajas under the reigns of Haider Ali and his son, Tipu Sultan (from WP):
- (Immadi) Krishnaraja Wodeyar II (1734–1766), puppet ruler under Hyder Ali from 1761
- Nanjaraja Wodeyar (1766–1772), puppet ruler under Hyder Ali
- Bettada Chamaraja Wodeyar VIII (1772–1776), puppet ruler under Hyder Ali
- Khasa Chamaraja Wodeyar IX (1776–1796), puppet ruler under Hyder Ali until 1782, then under Tipu Sultan until his deposition in 1796.
By Tipu's wish, there was no maharaja, traditionally of the Wadiyar dynasty, from 1796 to 1799. Krishnaraja Wadiyar III succeeded after Tipu's overthrow in 1799 at the age of five.
Haider Ali was the Sarvādhikārī of Mysore from 1761 onwards, and Tipu Sultan took over this title on his father's death:
Sarvādhikārī is a title with diverse uses in India, including an old title for the Chief minister of a southern Indian ruler, notably of the hereditary Maharaja of Mysore; this was the office Tipu Sultan succeeded his father Hyder Ali and established a Muslim empire called Khudadad.
WP's source describes Haider Ali's styling:
H.E. Shams ul-Mulk, Amir ud-Daula, Nawab Hyder 'Ali Khan Bahadur, Hyder Jang, Nawab of Hydernagar, Subadar of the Carnatic Balaghat, Suba of Sira, and Sarvadhikari of Mysore .... Sipah Salar (C-in-C) after 19th June 1758, and Suba of Sira from 1761. ... Effectively seized power and adopted the title of Sarvadhikari or Chief Minister of Mysore 1761. ... Prom. to the titles of Shams ul-Mulk, Amir ud-Daula, Hyder Jang and Subadar of the Carnatic Balaghat* ...
* these titles are assigned to Hyder 'Ali by Kirmani on the title page of his Hishan-i-Hyduri, but no other evidence has been found, either in the Mughal records or those of Hyderabad and Mysore.
The same site also details the process of annexation, and how Haider Ali formally continued to rule through the succession of maharajas (spelling from the original):
A military genius, he rose to high commands under his masters, and for his efforts received extensive lands, honours and offices. Through guile and intrigue, he established control over the whole administration of the state, effectively seizing power in 1761 through appointment to the office of Sarvadhikari. He increased his powers further when the old Maharaja died, leaving three minor sons. The eldest of these succeeded under a regency headed by Hyder, who poisoned of his charge four years later, just before the regency was due to end. His younger brother followed, only to suffer the same fate. A third regency follwed when a young scion of the family succeeded through adoption by the mother of the recently two deceased, childless princes.
Which implies that it was relatively bloodless. Dalrymple's 'The Anarchy' refers to this as:
In the early 1760s he [Haidar Ali] deposed the reigning Wodiyar Raja of Mysore and seized control of his state in what today might be called a military coup...
Tipu Sultan started by continuing with his father's offices.
Tipu the Emperor
The same page also continues on how Tipu deposed the maharaja in 1786 (spelling from the original):
Tipu Sultan succeeded his father as Savadhikari in 1782. ... His administration set about eradicating Hindu influence throughout the region, traditional rulers were deposed, dispossessed or murdered and their territories seized, place names changed to Islamic derivatives, Muslim laws declared paramount, conversions "encouraged", a new calendar invented. Seing no use in continuing the charade of a regency, he deposed the Maharaja in 1786, assumed complete power and renamed his state Khudadad. Within a year, he had thrown off any semblance of allegiance to the Mughal Emperor, substituted his own name at Friday prayers, and proclaimed himself Padshah, declaring that the Emperor was now a prisoner of Scindia and a mere cipher.
A partisan "side" seems to have been taken in this description -- Dalrymple's 'The Anarchy' notes how Tipu Sultan offered many grants and donations to Hindu temples and brahmins (but it is outside the scope of this question). However, this is Dalrymple on the ascension of Tipu:
... Tipu then decided to break off relation with Shah Alam, so becoming the first Indian ruler formally to disown even a nominal sovereignty to the Mughal Emperor. He ordered that the Friday sermon, the khutbah, should be read in his own name not that of the Emperor...
The Wodeyar family were definitely not happy with this overthrow, as evidenced by his grandmother's (Maharani Lakshmi Ammani Devi) scheming to get Krishnaraja Wadiyar III re-appointed as the maharaja after the British took down Tipu.