Otherwise known as the “Tree of a Thousand Realms.” It is a clan of magi that originates from Northern Europe. The clan’s notable characteristic is that its Magic Crest is extremely diluted. Or, rather than diluted, it’s more like it hardly exists at all. Generally, a Crest is proof of a magus being the successor of their family and is passed down from generation to generation. There are also cases where the Crest is divided up, but it is fundamentally limited to close relatives.
However, just as its name implies, Yggdmillennia has thinly spread out its roots over a long time—in other words, the clan has lost most of the functions of its Crest and has chosen the method of increasing its members with families who are “Yggdmillennia” in name only. The important point is that the clan’s Crest is capable of being simply transplanted like a seal pasted onto an arm, even if the person is a complete stranger or they already have another Crest.
This Crest’s functions only allow for some slight sympathy between their spells and for determining whether or not someone is connected to “Yggdmillennia.” It is has lost any special characteristics it once had, but it is precisely this last remaining universal function that aid the abnormal increase in Yggdmillennia clan members.
Yggdmillennia swelled up in size by gathering up families who have been forced out of the world of magi, such as families whose Magic Circuits are gradually deteriorating away, families who have lost their Magic Crests in accidents or families who lost in political conflicts.
Of course, even if any of them attain Sorcery or reach the Root, it will never turn into praise for Yggdmillennia itself, but—just having their desire to “have their name remembered in history” investigated by others may be the proof of this diluted clan known as Yggdmillennia having existed.
In truth, quite a number of magi are included in Yggdmillennia under the table in the world of Fate/Apocrypha. Many of the magi who cause subspecies Holy Grail Wars are connected to Yggdmillennia. It goes without saying that it was for the sake of collecting data on the Holy Grail War.
The current leader is Darnic Prestone Yggdmillennia. The leader after the end of the novels is Caules Forvedge Yggdmillennia.

Fate/Apocrypha material: Fate/Apocrypha Encylopedia