Matilda was built in France and launched in 1779. She was first used as a whaling ship and in 1791 transported convicts to Australia in 1791. 
February 18. - The Mary Anne, bound to Botany Bay, sailed from Gravesend with near 100 women convicts on board. The Matilda also sailed at the same time to receive convicts at Portsmouth. Two other ships have sailed within these nine days, the William and Anne, and the Britannia, both with men convicts, supposed to have on board about 200 each. The other ships still lying at Gravesend, to receive the men convicts from Newgate, are the Albemarle, the Barrington, and the Active...
The above ships together with Atlantic, Salamander, Gorgon and Queen became known as the Third Fleet.
The Mary Ann departed England in February 1791 and the rest of the fleet departed in March 1791 and later met with the Queen from Cork at Madeira.
Active, Admiral Barrington, Albemarle, Britannia and Matilda departed from Portsmouth; their naval agent was Lieutenant Robert Parry Young. HMS Gorgon sailed from Portsmouth on 18th March 1791.
Atlantic, Salamander, and William and Ann departed from Plymouth; naval agent was Lieutenant Bowen.
Queen departed from Cork, Ireland; naval agent, Lieutenant Samuel Blow.
David Collin's account of the arrival of the Third Fleet.....
On Monday, the 1st of August, the Matilda arrived in Port Jackson, after an extraordinary passage of four months and five days from Portsmouth; having sailed from thence on the 27th of March, with four sail of transports, with whom she parted company that night off Dunnoze. Another division of the transports had sailed a week before from Plymouth Sound. On board the Matilda on arrival were two hundred and five male convicts; one ensign, one serjeant, one corporal, one drummer, and nineteen privates, of the New South Wales corps; and some stores and provisions calculated as a supply for the above number for nine months after their arrival.
The master of this ship had anchored for two days in a bay of one of Schoeten's Islands, distant .from the main land about twelve miles, in the latitude of 42 0 15' S; where, according to his report, five or six ships might find shelter. Those who were on shore saw the footsteps of different kinds of animals and traces of natives, such as huts, fires, broken spears, and the instrument which they use for throwing the spear. They spoke of the soil as sandy, and observed that the ground was covered with shrubs resembling those found at Sydney.
The convicts in this ship, on their landing, appeared to be aged and Infirm, the state in which they were said to have been embarked. It was not therefore to be wondered at, that they had buried twenty-five on their passage. Twenty were sick, and were immediately landed at the hospital. Fifty-five of the convicts brought in this ship, selected from the others as tanners and artisicers, were sent up to Parramatta; of the remainder, those whose health would permit them to go were put on board the Mary Ann, together with thirty-two convicts of bad character from among those who came out in the preceding year, and eleven privates of the New South Wales corps. On the 8th, the Mary Ann sailed for Norfolk Island. 
The Matilda departed Port Jackson in November 1791 bound for Tahiti which she reached on February 14, 1792, anchoring in Vaitepiha Bay but remaining only a short time. On the night of February 24, 1792, the Matilda foundered on Mururoa atoll, 640 miles south-east of Tahiti. The crew were saved and returned Tahiti on 5th March 1792.
NOTES AND LINKS
1). Condition of the convicts received in the colony in the Third Fleet - Governor Phillip to Lord Grenville
2). Convict arriving on Matilda, Daniel Phillips accompanied John Howe on his expedition of discovery in 1819.
3). Gilbert Grant arrived as a convict on the Matilda. He died in November 1813 aged 60 and was buried in the Old Sydney Burial Ground.
4). Some of the vessels of the Third Fleet were to proceed to the Southern Whale Fisheries after unloading the prisoners; the rest were bound for Bengal where they were to be freighted back to England with cotton. The sailors on board the Nootka ships were to have nine guineas for the run to Botany Bay after which they were to share as whale fishermen do. The other sailors were paid twenty five shillings per month. (The Times 15 March 1791)
5). Read more about the Matilda in George Vancouver's account A Voyage of Discovery to the North Pacific Ocean ....... Lieut. Hanson of the Dædalus was instructed to call at Otaheite on his voyage to Port Jackson not only to procure refreshments but to receive onboard twenty-one English seamen who had been cast away in the ship Matilda, of London, on the 25th of February, 1792, on a ledge of rocks, not within sight of any land. After this unfortunate accident the crew returned in their boats to Otaheite; from whence, six days before, they had departed in the ship. From Otaheite, the second mate and two of the sailors had, in one of their open whale boats, proceeded towards New South Wales. The rest of the crew remained on the island, excepting Mr. Matthew Weatherhead the commander of the vessel, who, with two men and two boys, had taken their passage from Otaheite on board the Jenny of Bristol; and on their arrival at Nootka, Senr* Quadra not only provided Mr. Weatherhead with a passage towards England through New Spain, but benevolently furnished him with a sum of money to defray his expenses through a country where the inhabitants would necessarily be strangers to himself and all his connections.
The misfortune of this shipwreck appeared to have been attended with very unpleasant consequences to our friends at Otaheite. The few valuable articles which these unfortunate people had been able to save from the wreck, instead of having been secured and properly taken care of, had been indiscriminately dispersed, or left to the disposal of the natives. This had produced a jealousy between the chiefs of Matavai and those of Oparre; and on their disagreement concerning the division of the spoil, some of the Englishmen had sided with the chiefs of the one party, whilst others had taken up the cause of the other. A war was the necessary consequence between the two districts, which had terminated very disastrously for Matavai. Nearly the whole of that beautiful district had been laid waste, their houses burnt down, and their fruit-trees torn up by the roots, and otherways destroyed. This was the sum of what I was able to learn; but the very confused and incoherent detail that was given me of all these transactions, prevented my acquiring any satisfactory information on this melancholy event.
6). Hunter Valley convicts/ passengers arriving on the Matilda in 1791
7). Jonas Bradley Sergeant of the 102nd regiment arrived free on the Matilda.
8). Convicts and passengers of Matilda mentioned in Colonial Secretary's Papers - Special Bundles......
John Anslip - Constable in Sydney
Samuel Oaken Baker was on the list of convicts who received an Absolute Pardon (January 1813)
William Horsford of Hawkesbury; John Booth of Portland Heads; Henry Hyams of Hawkesbury; Stephen Richardson of Richmond; Daniel Phillips of Hawkesbury; Adam Bell of Hawkesbury - All on list of persons who came as convicts and who claimed they were free at the last General Muster, without supporting documentation.
James Fletcher - On list of all grants and leases of land registered in the Colonial Secretary's Office
George Johnson - Received Certificate of Freedom. To be struck off victualling list 22 May 1813
John Love - Came Free. Sentenced to Newcastle penal settlement 31 December 1816 for cattle stealing
Joseph Maund - On list of all grants and leases of land registered in the Colonial Secretary's Office 4 June 1804
Thomas Moxham - of Portland Head
William Pantony - Deceased. On return of persons indebted to Government for cattle issued from the Government Herds, to be paid for in cash or grain; appears as Pentony - 13 April 1819
Thomas Sanders - Baker at the Rocks; landowner at Prospect. Memorial - January 1810
James Shepherd - of Kissing Point
Daniel Smallman of Hawkesbury
John Tarlington of Prospect
 The Lady's Magazine: Or Entertaining Companion for the Fair Sex ..., Volume 22
 Historical Records 2. Historical Records of Australia, Vol.1, p. 225
 An Account of the English Colony in New South Wales: From Its First ... By David Collins, Philip Gidley King, George Bass, p.139
 Historical Records of Australia, Vol.1, p225