
überliefern
to pass down
To pass on knowledge, stories, customs, or traditions from one generation to the next so that they are preserved.
Diese Legende wurde über Jahrhunderte mündlich überliefert.
This legend was passed down orally over centuries.
to pass down / hand over
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to pass down
To pass on knowledge, stories, customs, or traditions from one generation to the next so that they are preserved.
Diese Legende wurde über Jahrhunderte mündlich überliefert.
This legend was passed down orally over centuries.

to hand over
To deliver or hand over a person or thing to someone. This meaning is formal or historical.
Der Deserteur wurde den feindlichen Truppen überliefert.
The deserter was handed over to the enemy troops.
'Überliefern' (to pass down / hand over) is an inseparable verb because the prefix 'über-' is unstressed. The prefix remains directly connected to the verb in all sentence forms.
Man überlieferte die alten Mythen von Generation zu Generation.
The old myths were passed down from generation to generation.
'Überliefern' (to pass down) is used especially often in the passive to emphasize that a piece of information comes from the past. A typical formulation is 'es ist überliefert, dass ...' (it has been passed down that ... / tradition has it that ...).
Es ist überliefert, dass der König sehr weise war.
It has been passed down that the king was very wise.
This verb is almost always combined with immaterial things such as 'Geschichten' (stories), 'Wissen' (knowledge), 'Traditionen' (traditions), 'Bräuchen' (customs), or 'Sagen' (legends).
Die Rezepte wurden in der Familie mündlich überliefert.
The recipes were passed down orally in the family.
The meaning 'jemanden ausliefern' (to extradite someone / hand someone over) is very rare today and belongs to formal or historical language. You mainly find it in historical texts or novels.
Der Gefangene wurde dem Gericht überliefert.
The prisoner was handed over to the court.
to hand over / to vomit
Both verbs can describe the formal handover of a person or thing to someone else. Übergeben is the usual form today, while überliefern sounds elevated or historical in this meaning. For an ordinary handover today, use übergeben; überliefern may be appropriate in a historical account.

Der Ritter überlieferte die wichtige Urkunde dem König.
The knight delivered the important document to the king.
Der Kurier übergab die wichtige Urkunde dem Bürgermeister.
The courier handed the important document to the mayor.