I don't have a comprehensive answer to this, after all, the Middle Ages is a long period, and there would have been a lot of variation as you say, but it did remind me of this article I read recently about Henry V.

In August 1415, Henry V and his army invaded France, in order to resume the war against the French. If you read the older books it's claimed that "He strengthened the fleet, both by increased warship construction and by obtaining ships from the Netherlands and Spain- some 1,500 vessels were used in the task of transporting the army across the English Channel". This is from the "Chronicle of Britain", 1992.

As you can see, the article I linked to claims that this number is exaggerated, and that there were far fewer ships, but it was "a fleet of mainly English ships with foreign vessels hired or commandeered to join the expedition".

From the article: "Lambert believes that Henry eventually assembled about 650 ships, with about 50 more put to sea to protect the fleet. He spent more than £7,000 from February to May hiring ships from Holland and Zealand, a vast sum but one that may have brought in no more than 245 ships, fewer than Henry had hoped. In March, his admiral, the Earl of Dorset, was told to commandeer all English ships over 20 tons and get them to Southampton by May. In April, further orders were issued to seize all ships including foreign vessels from the mouth of the Thames to Newcastle, and from the ports along the south coast to Bristol. In July, ships in London over 20 tons were also seized".

"Foreign ships were hired at three shillings, four pence a ton for every three months, plus the crew’s wages, while English ships were requisitioned – despite repeated bitter protests by ship owners – at two shillings a ton plus wages".

So it seems that medieval kings, at least, could requisition and commandeer ships for their own purposes, as well as purchasing them outright. Whether it would work like that for a lesser noble I don't know.

This page from the Agincourt 600 website says "In this period the number of royal ships owned by the king was too small to provide enough vessels for overseas expeditions. Instead private ships were hired or (much more commonly) impressed into service to make up the great bulk of the fleet necessary to transport thousands of men and horses to France. Royal agents would be sent into ports with powers to arrest vessels and crews (as we will see over the course of the year). There was often hostility displayed towards these officials, with two sergeants-at-arms forced to take refuge in a barn in Wells in Norfolk in 1380. These demands by the king often placed a heavy burden on local communities, with the wages of sailors in royal service often in arrears and with ship owners running the risk of losing their valuable vessels in war. A small number of additional ships were provided by the federation of the Cinque Ports for fifteen days service". citation is "Calendar of the Patent Rolls 1413-1416, pp. 293-4; J. W. Sherborne, ‘The Hundred Years’ War. The English Navy: Shipping and Manpower’, Past & Present, 37 (1967), pp. 164-5"

But the same site goes on to say: "Nowadays historians are reluctant to recognise Henry V as one of the founders of the Royal Navy, because the word ‘navy’ was not used in the modern sense until the 16th century and ‘the Royal Navy’ implies the existence of a standing fleet of royal ships, when no medieval monarch possessed one (nor for that matter was there a standing army).

In addition, it was impossible to exercise true sea power in medieval times, because the ships of the day found it difficult to keep the sea, let alone intercept an enemy. Lastly, there was no continuity between the fleet of Henry V and that of Henry VIII (the next monarch with a claim to be the founder) since nearly all the royal ships which Henry V had were sold soon after his death".

So, at the risk of relying too heavily on one example (Henry V 600 years ago), I'd say that the evidence is that navies didn't become official institutions set up by states until late in the Middle Ages, and that sometimes kings did indeed requisition and commandeer ships by force.

100 years after Henry V's time Scotland and England both had navies and engaged in a sort of game of one-upmanship. Scotland built the Great Michael, the largest ship in the world in 1511, but it was superseded by Henry VIII's Henri Grâce à Dieu in 1512.

In Norway there was the leidang system, by which the country was divided into ship-districts, each responsible for maintaining, provisioning, and outfitting a ship with a specified number of oars - and oarsmen, who would also fight. In 1277 Norway had 279 such ship-districts. The King could call out the leidang for a few months if he was attacking someone else; for defense against invasion the term of service could be longer. At the height of Norwegian power in the eleventh and twelfth centuries, the leidang seems to have been the main source of manpower for foreign wars. Later the system declined through not being used as often. The last time the leidang was called out for war was against the Victual Brotherhood in 1429, and the small Norwegian ships fared rather badly against the tall cogs. However, a "leidang tax", paid in lieu of the militia service, was collected as late as 1836.

Sources (in Norwegian):

• Per Sveaas Andersen, article in Store Norske Leksikon.
• Øyvind Flatnes, Master's thesis, Leidangen i operativ tjeneste.

A bit later than your period, but I wrote a piece here on Ottoman galley warfare (and the role played by the empire's Islamic character, though that's not your interest).

Essentially, galleys' short operating range (large crew, shallow draft = limited supplies) required the acquisition of forward bases in the form of harbours/ports protected by fortifications. These bases would allow your fleet to operate in an area of interest for extended periods of time, as well as allowing it to jump from base to base until you're at the end of your "chain" of bases.

The conquering of such bases would often require a combined army-navy effort: an army from the landward side, and a fleet from the sea. This siege of the fortification to be captured was generally successful, as aid could rarely be summoned, especially if surprise was achieved and no distress messengers could be sent out.

The Scandinavians (until 12th century) tied their boats together and crashed into the enemy fleet.

The style of fight changed when Sverre Sigurdssson in the 12th century wanted become King of Norway and claimed being a son of a king. He basically joined the bloody civil war. he was born on the Faroes and he had an education as a priest, which was at that the best you could get and was well orientated about new European developments on weapon technologies.

With small group of mercenaries he began his relentless work to become king. Fleets didn't become tied together and he commanded sometimes the battle from a small rowing boat. His small group of mercenaries was equipped with latest technology aka armor, which made them able to control large areas with peasants, which were at that time equipped with armor and weapons. He gave his own people and people who joined him land of dead enemies and important positions. Most of them were sons of peasants. Most of the aristocracy died in battles in these years and the aristocracy vanished. Kingdom at that time was equal to having influence by force. All regions were self sufficient and local assemblies of peasants on a thing were enough to solve problems. A king demands taxes which wasn't of course very popular. All regions had to prepare for war by equipping boats with men called leidang These forces could be a help or a thread in the case a region changes the side.

Source: Norges Historie, Aschehoug Forlag

Skimmed bits and pieces of this and could contribute a bit to the Mediterranean section if asked, but I just wanted to add that there is an absolutely wonderful edited volume on this topic titled, War at Sea in the Middle Ages and the Renaissance if you wanted to read more. It's edited by Unger and Hattendorf.