Supreme Cores was the title that Garrick Ollivander, the noted wandmaker and owner of Ollivanders, gave to the three kinds of wand cores that he believed to be the best. These were the only cores that he used in his wands, though other makers might still use other cores.
Unicorn hair generally produced the most consistent magic, and was least subject to fluctuations and blockages. Wands with unicorn cores were generally the most difficult to turn to the Dark Arts. They were the most faithful of all wands, and usually remained strongly attached to their first owner, irrespective of whether he or she was an accomplished witch or wizard.
Minor disadvantages of unicorn hair were that they did not make the most powerful wands (although the wand wood might compensate) and that they were prone to melancholy if seriously mishandled, meaning that the hair might 'die' and need replacing.
As a rule, dragon heartstrings produced wands with the most power, and which were capable of the most flamboyant spells. Dragon wands tended to learn more quickly than other types. While they could change allegiance if won from their original master, they always bonded strongly with the current owner.
The dragon wand tended to be easiest to turn to the Dark Arts, though it would not incline that way of its own accord. It was also the most prone of the three cores to accidents, being somewhat temperamental.
This was one of the rarest core types. Phoenix feathers were capable of the greatest range of magic, though they might take longer than either unicorn or dragon cores to reveal this. They showed the most initiative, sometimes acting of their own accord, a quality that many witches and wizards disliked.
Phoenix feather wands were always the pickiest when it came to potential owners, for the creature from which they were taken was one of the most independent and detached in the world. These wands were the hardest to tame and to personalise, and their allegiance was usually hard to win.