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The procedures surrounding this varied a lot by country and time and place but typically in the 17th-18th centuries there wasn't much of a rigid legal procedure that was followed.

The mid-17th century Caribbean was famous for the totally corrupt English and French governors who unscrupulously sold privateering commissions/letters of marque to anyone who could pay, often whether or not there was actually a war going on. Even when buccaneers didn't have ostensibly valid commissions at all, they would commonly just continue using outdated ones or lie and claim they had them when attacking a ship, and they could easily get away with this by paying off the same local governors who sold them their phony or semi-legal commissions in the first place and profited off their plunder. The line between privateer and pirate was often very fuzzy and that's what the term "buccaneer" mainly describes. Famous "pirate havens" like Tortuga and Port Royal were based on this type of corrupt relationship between buccaneers and local authorities which essentially gave the buccaneers or "privateers" free reign in the Caribbean to plunder what they liked even in times of peace as long as they stayed away from ships of their own nation. I made another post that talks more about this.

As for how plunder was divided up, buccaneers had a system for that but the government was usually cut out of it. They also didn't have any standard pay. Nearly all privateers famously operated according to the expression "No prey, no pay" meaning that the only payment they could expect was plunder from what they captured. And they wouldn't return to port to divide up their loot either because they didn't have to. Instead they would almost always either do it at sea or go to some isolated beach or cay or island where they didn't have to be under the watchful eye of any government officials. The former French buccaneer Alexandre Exquemelin in his book The Buccaneers of America published in 1678 describes the custom for buccaneering voyages like this:

When the provisions are on board and the ship is ready to sail, the buccaneers resolve by common vote where they shall cruise. They also draw up an agreement or chasse partie, in which is specified what the captain shall have for himself and for the use of his vessel. Usually they agree on the following terms. Providing they capture a prize, first of all these amounts would be deducted from the whole capital. The hunter's pay would generally be 200 pieces of eight. The carpenter, for his work in repairing and fitting out the ship, would be paid 100 or 150 pieces of eight. The surgeon would receive 200 or 250 pieces of eight for his medical supplies, according to the size of the ship.

Then came the agreed rewards for the wounded, who might have lost a limb or suffered other injuries. They would be compensated as follows: for the loss of a right arm, 600 pieces of eight or six slaves; for a left arm, 500 pieces of eight or five slaves. The loss of a right leg also brought 500 pieces of eight or five slaves in compensation; a left leg, 400 or four slaves; an eye, 100 or one slave, and the same award was made for the loss of a finger. If a man lost the use of an arm, he would get as much as if it had been cut off, and a severe internal injury which meant the victim had to have a pipe inserted in his body would earn 500 pieces of eight or five slaves in recompense.

These amounts having first been withdrawn from the capital, the rest of the prize would be divided into as many portions as men on the ship. The captain draws four or five men's portions for the use of his ship, perhaps even more, and two portions for himself. The rest of the men share uniformly, and the boys get half a man's share.

When a ship has been captured, the men decide whether the captain should keep it or not: if the prize is better than their own vessel, they take it and set fire to the other. When a ship is robbed, nobody must plunder and keep his loot to himself. Everything taken -- money, jewels, precious stones and goods -- must be shared among them all, without any man enjoying a penny more than his fair share. To prevent deceit, before the booty is distributed everyone has to swear an oath on the Bible that he has not kept for himself so much as the value of a sixpence, whether in silk, linen, wool, gold, silver, jewels, clothes or shot, from all the capture. And should any man be found to have made a false oath, he would be banished from the rovers, and never more be allowed in their company.

From that last part, you can see how ships themselves were not always the main prize and they wouldn't always be brought back to port (the main prize was usually the money and cargo and slaves that a ship carried). Exquemelin says that buccaneers would either burn the captured ship or switch their ship for that before burning it, but when they were feeling friendlier buccaneers would sometimes simply give the ship back to the captured crew after looting it and send them on their way -- there are many examples of this. Other times, if the buccaneers had an excess of crew or they wanted to keep both ships, they might split into two companies with each taking command of one ship.

When buccaneers eventually did return to ports such as Tortuga or Petit-Goâve or Port Royal to spend their plunder, all they would pretty much have to do is say they captured it legitimately and no one would bring them to trial, least of all the governor who they were most likely paying off with a cut of their plunder. The Spanish, who were by far the most common targets of both English and French buccaneers, often bitterly complained at being attacked liked this even when there wasn't a war going on, but prior to 1670 their complaints pretty much got laughed off and ignored by local governors and the English and French governments. Even after 1670, Charles II of England tacitly condoned many buccaneers like Henry Morgan, who sacked the Spanish city of Panama in 1671 in clear violation of the 1670 Treaty of Madrid, and actually knighted him in 1674 before making him the new governor of Jamaica where he served until his death in 1688. Charles II also granted a royal pardon to the buccaneer Bartholomew Sharp and others in 1682 after they had spent several years plundering Spanish possessions along the Pacific coasts of America, again despite there being no war. Probably one reason Charles II did this in the latter case was because Bartholomew Sharp along with his compatriots (Basil Ringrose, William Dampier and others) were among the first Englishmen to penetrate and explore the Pacific Ocean since Sir Francis Drake and Thomas Cavendish had a century earlier, and they all published extensive and valuable descriptions of their voyages soon after returning to England.