First off, I should probably ask the classic AskHistorians question of ‘what duchies, where and when?’ The answer can be radically different based on the time period, region/country, and what specific duchies you’re curious about.

So let’s start with, what is a duchy in the first place? A relatively common title in later medieval Europe, in the early 1100s (which is what I’ll focus on) there were comparably few ‘dukes’ as opposed to later on, say in the late 15th century. The title, which stems from the Latin position of ‘dux’ had developed during the early medieval period, following the collapse of Roman Authority in the West, to represent a sort of intermediary between the already powerful regional counts (stemming from Latin Comes) and the person of the King, who following Charlemagnes example were at least hypothetically the highest authority in the realm.

Now, especially in the early part of the period we are discussing, Duke was not a title used very widely. In England, for instance, it is completely unknown until much later - the comparable large magnates were instead known as ‘Earls’ which stemmed from the Norse Jarls and carried a tradition of the earlier English Ealdormen. Because of the relatively centralised nature of the English state at the time, these Earls (before the conquest at least) were hypothetically ruling only at the Kings behalf, and the position was technically not hereditary. The trend towards the end of the Saxon period however was one of large families consolidating their hold over the large Earldoms at the expense of royal authority, so similar in some ways to what had already occurred on the continent. In Ireland however, you had varying levels of kings, sub kings and lords that completely excluded the title duke, and similarly in Scotland the title Duke is not used, in favor of titles like Earl, Mormaer and Lord.

Forgive my digression. The key point is that following the Norman conquest, the role of Earl in England changes significantly from its original sense of royally appointed administrator, albeit from noble lineage, to a title held by a noble, by grant of the King but without many of the responsibilities that had originally been a part of the job. Many Earls in the Norman period held little to no actual land in their own Earldoms - leading to situations like the Earl of Surrey, who was commonly called the Earl Warenne after his family name, instead of the earldom he was entitled to.

So that’s the first part of my answer, which is that while still responsible, in principle, for some of the justice done in their earldom, many Earls were rather very rich magnates, given a title as a result of favor of the King or a reward for loyalty etc. They may rarely even visit their earldom, and prefer to perambulate their estates that very well may be on the other side of the channel. They were still able to collect the various fines and taxes due them from the ‘justice’ they provided to their ‘subjects’ however, which gives us some idea why such a grant by the King would very well be sought after.

Now, said Earl probably owns a lot a land in other areas. So the Earl of Gloucester, during the reign of Edward I, was a major marcher lord on the welsh border. This meant that his lordship of Glamorgan was in addition to his holding the Earldom of Gloucester. It gets even messier when you consider that during much of the medieval period in England a marcher lord was almost exempt from the laws and regulations of the kingdom - he was essentially endowed with the power of a King in his own lands, saving the power to rebel. That means that The Earl might have to do homage and pay taxes etc. For his Earldom, but had a very free hand in his lordship of Glamorgan.

What’s even crazier is when you start looking at the Church as well. Bishops were hypothetically religious prelates who were responsible for the administration of the spiritual health of their bishoprics. These bishoprics however had become rich through the donation of lands by various lords and kings, and so becoming bishop of Winchester, for instance, could make one fabulously wealthy. Stephen if Blois made his brother, Henry, Abbott of Glastonbury and Bishop Of Winchester, Cast making him one of the wealthiest men in England. Some Bishops attained numerous bishoprics, leaving the day to day administration often in the hands of arch deacons and using the proceeds to pay the political game of court.

Even weirder was the case of Kings like William Rufus, who could collect the revenues of absent bishoprics without appointing a new bishop. This practice proved popular but led to the great investiture controversy between secular lords and the Pope.

So what have we learned through this web? A duke, Earl or Count often was a large landholder who was not always that tied to their own title, beyond the prestige and wealth it brought them through the administration of justice. Their title could be granted by the King of passed hereditarily, but the administration was often left in the hands of lower down sheriffs, seneschals and prevots. Titles were sometimes just that - a title given to increase prestige but if it wasn’t backed up by commensurate lands and castles then it lacked some meaning. Giving a man an Earldom didn’t make him lord of all those lands, as in all the inhabitants of The area suddenly were solely responsible to him in all ways. Instead he was now owed some of the proceeds of justice in the area, and gained the prestige of the title.

To illustrate my last point, my favourite example is that during the War of the Roses, the Duke Of York held hardly any lands or sway in York itself or the surrounding area, and when he took the city the inhabitants were openly hostile as they had long been loyal to the Lancaster family.

I’ll post more sources when I’m off my phone, but a great book I almost always recommend is Frank Barlow’s Feudal Kingdom Of England, 1042-1216.