It is a common trope on popular TV shows that mighty lords have to deal with endless strings of people coming to them to ask for justice. Those scenes often display a very young lord who's quite unaware on how to proceed. A faithful or treacherous advisers reaches his ear and whispers something. The young lord, as a character, is being tested. What will he do? How will he solve the problem? How will he deal with the emotions thrown at him? As far as character development goes, this is an interesting scene. As far as history goes, this is rather cliché.

When Jean de Joinville reminisced the "good old time" (meaning, the 12th century) he pictured Louis IX of France, aka saint Louis, distributing justice under a tree. This scene ranks among the most well-known anecdotes of the French history. Most French people have heard about it as kids at school. There he was, saint Louis, giving justice himself. Sitting under a tree.

Was he sitting, though? Joinville says nothing of the sort exactly. There was a tree, alright, but the king would also walk around and see how his many delegates were dealing with the matters brought to them. When you read the text closely, you realize that saint Louis, in fact, was supervising the proceedings. He micro-managed a few cases when necessary but he was mostly watching justice being done in his name rather than serving it himself. Joinville, nevertheless, stresses how king Louis talked "from his mouth" on several cases. His word was his command and he was physically there to give it himself.

It was commonly understood that the king couldn't be everywhere at once. However, until the end of the Middle Ages, he certainly moved around a lot. The most important fact, though, was that justice (and the shedding of blood) was his priviledge and his only. Even the Church couldn't burn someone at the stakes. The Church could say that someone was unfit to be a part of society because he or she was a heretic, a sodomite, or else, but it was still the king's officials who carried the sentence. Always. In the king's good name.

Since we're in France, let's stay there for a while and make it our case study.

We need to distinguish the difference between feudal law and manorial law. Feudal law established the relationship between vassals and their suzerain. Manorial law (which is how I translate "droit seigneurial") was the law biding people to the lord of their land. Depending on the nature of the crime, people would be judged by their lord, the lord of their lord, or the king himself. A distinction was made between low, middle and high justice.

Since the king couldn't be everywhere, he had representatives to carry justice in his name. They had different names depending on the regions: bailli, sénéchal, prévôt, etc. Jean de Joinville had himself occupied such a function when he was sénéchal of Champagne. He didn't operate alone, he worked as part of an intricated system. The people who advertized others they were to come to court (either by yelling on the market place or handing out written orders) where the sergeants. There was a whole system.

Mighty vassals, of course, didn't like that the king's official were keeping an eye on their own backyard and they were many disputes as to who was abilitated to deal such or such judicial cases. Nevertheless, as society became more and more sophisticated with the growing of cities and the multiplication of town and guild charters, the exercise of the law became more and more of a trade. Judges, lawyers, clerks, etc. were expected to have attended the university, to read and write Latin and have studied the numerous legislative systems that were enforced within the realm.

By the 14th century, law was a matter of experts and the king of France created the parliament, a specialised entity within his court, which was the higher judicial court of the land and which sole purpose was to deal with the many appeals he received everyday. Though the system had been different in England and in other countries, this tendency was confirmed everywhere. The law was becoming less and less personal. It was now the tool of bureaucrats.

In later centuries, those bureaucrats became a new counter-power to the king's authority. They grew far more dangerous politically speaking than the old nobility. It also became exceedingly rare that kings would carry justice themselves, one famous exception to that rule being Louis XIV of France who was the last French king who dared to sit at parliament and actually listen, supervise and challenge what was being done in his name.

In conclusion, for a king to interfere himself with a judicial matter between the 12th and the 15th century, it already had to be a very important matter (meaning, involving powerful lords). Common lords were more exposed to day-by-day local and bloodless disputes. However, even them ended up appointing representatives or stewards to deal with such matters since they also had to roam the realm on many occasions. Many a times, their wives would fill in their stead and see the job done. A lady was just as good as a lord when justice had to be dealt with. It wasn't too rare for ladies and lords to travel strategically in a coordinated manner to cover all of their estates, seldom meeting each other on grand occasions.

Addendum. As for thrones, let's simply say that they were overrated. People prefered kings who walked among them and mingled. Richard II of England was quickly despised and hated for his obsession of sitting above and away from everybody else. He was met with a quick end. Sitting on a throne is more of a modern than a medieval thing. Same with harsh sentencing. Cutting hands and legs wasn't the go-to option for judges in the Middle Ages. The Tudors, however, were quite fond of it.

Second addendum. About thrones again (after re-reading some old notes), justice was more often rendered in front of churches! A very logical location indeed since the Last Judgment was often depicted over the main entrance door.