
übergeben
to hand over
To give something to someone, usually in a formal or official way; to hand something over.
Bei der Feier wurde dem Gewinner ein Scheck übergeben.
At the ceremony, a check was handed over to the winner.
to hand over / to vomit
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to hand over
To give something to someone, usually in a formal or official way; to hand something over.
Bei der Feier wurde dem Gewinner ein Scheck übergeben.
At the ceremony, a check was handed over to the winner.

to vomit
To expel stomach contents through the mouth; to throw up.
Dem Kind wurde auf der langen Autofahrt schlecht und es musste sich übergeben.
The child felt sick on the long car ride and had to vomit.

to hand over
To pass on a task, office, or responsibility to another person.
Der alte Geschäftsführer hat die Leitung der Firma an seinen Sohn übergeben.
The old managing director handed over the management of the company to his son.

to surrender
To hand something or someone over to an authority or an enemy; to capitulate.
Die belagerte Stadt wurde schließlich dem Feind übergeben.
The besieged city was finally surrendered to the enemy.
'Übergeben' (to hand over/to vomit) is an inseparable verb. The prefix 'über-' always stays attached to the verb and is not stressed. The stress is on the second syllable: über-GE-ben.
Er übergab mir die Dokumente am Ende des Gesprächs.
He handed me the documents at the end of the conversation.
In most meanings, except 'sich übergeben' (to vomit), the verb needs two objects: the person receiving something is in the dative, and the thing being given is in the accusative.
Der Präsident übergab dem Sieger (Dativ) die Medaille (Akkusativ).
The president handed the winner (dative) the medal (accusative).
The meaning 'erbrechen' (to vomit) exists only when the verb is used reflexively with 'sich'. Without the reflexive pronoun, 'übergeben' never has this meaning.
Mir wurde plötzlich so schlecht, dass ich mich übergeben musste.
I suddenly felt so sick that I had to vomit.
The exact meaning depends heavily on the object. A concrete object points to 'aushändigen' (to hand over) (m01), a company or an office to 'Verantwortung weitergeben' (to pass on responsibility) (m03), and a city or fortress to 'kapitulieren' (to surrender/capitulate) (m04).
Der Kapitän weigerte sich, das Schiff zu übergeben.
The captain refused to surrender the ship.
to transmit / transfer
In a figurative sense, übertragen emphasizes assigning someone a task or responsibility. Übergeben places more emphasis on the change from the previous holder to the new person, often as a concrete handover. Use übertragen when assigning someone a task, and übergeben often when responsibility is changing hands.

Der bisherige Leiter übergibt Lara das Projekt vor seinem Abschied.
The previous manager hands the project over to Lara before his departure.
Die Chefin überträgt Lara die Verantwortung für das Projekt.
The manager assigns Lara responsibility for the project.