Much depends on how you define nobility. In Europe, anyway, nobility was a quality of blood, quite literally. Today we would say it's in the DNA--a quality of existence independent of behavior or of external validation. Marrying outside nobility literally diluted the purity of the blood and required several generations to restore.
But people often confuse nobility with titles, and titles did need a monarch. This was more true in some places than in others. By the time we're in Norman England, for example, the crown was the source of all titles. By the time of ... the Tudors? ... even noble status had to be granted from above.
France was more complicated (of course). The greater titles--particularly duke and count--were not only granted by the king but could be revoked by the king. In theory, the king could even make a commoner a count, but I don't believe that was ever done. But almost anyone could be made a "sieur" (we would call this a knight). Curious side note: the word knight derives from Knecht, which in German translates to "boy" or "servant". Roughly equivalent to garçon in French. The German for knight is Ritter. Which means rider. Which has the same sense as caballero in Spanish, or chevalier in French. All three languages basically have "guy who rides a horse." But the English just had to do things differently.
Anyways.
Down in Italy, nobles got some titles from the Emperor (who was also King of Italy), and a few from the Pope, but they did not hesitate to bestow titles on themselves. I confess I'm not sure how it worked in the Iberian peninsula, nor over in Hungary or Poland. But the general rule is easy: there was no general rule. Welcome to the Middle Ages!
But people often confuse nobility with titles, and titles did need a monarch. This was more true in some places than in others. By the time we're in Norman England, for example, the crown was the source of all titles. By the time of ... the Tudors? ... even noble status had to be granted from above.
France was more complicated (of course). The greater titles--particularly duke and count--were not only granted by the king but could be revoked by the king. In theory, the king could even make a commoner a count, but I don't believe that was ever done. But almost anyone could be made a "sieur" (we would call this a knight). Curious side note: the word knight derives from Knecht, which in German translates to "boy" or "servant". Roughly equivalent to garçon in French. The German for knight is Ritter. Which means rider. Which has the same sense as caballero in Spanish, or chevalier in French. All three languages basically have "guy who rides a horse." But the English just had to do things differently.
Anyways.
Down in Italy, nobles got some titles from the Emperor (who was also King of Italy), and a few from the Pope, but they did not hesitate to bestow titles on themselves. I confess I'm not sure how it worked in the Iberian peninsula, nor over in Hungary or Poland. But the general rule is easy: there was no general rule. Welcome to the Middle Ages!