abgeben
to hand in
To hand something over to someone or leave it at a particular place; to submit.
Die Studierenden müssen ihre Hausarbeiten bis Freitag abgeben.
The students have to hand in their term papers by Friday.

to hand in / give off
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to hand in
To hand something over to someone or leave it at a particular place; to submit.
Die Studierenden müssen ihre Hausarbeiten bis Freitag abgeben.
The students have to hand in their term papers by Friday.

'Abgeben' (to hand in/give off) is a separable verb. The prefix 'ab-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ich gebe das Formular morgen beim Amt ab.
I will hand in the form at the office tomorrow.
The verb consists of the prefix 'ab-' and the base verb 'geben' (to give). The prefix 'ab-' often has the meaning of 'away', 'down', or 'completed', which can be recognized in most meanings of 'abgeben' (to hand in/give off).
Kannst du mir bitte die Fernbedienung abgeben?
Can you please hand me the remote control?
In the context of submitting something, 'abgeben' (to hand in) is often used with official documents or assignments. Typical combinations are: 'eine Hausarbeit abgeben' (to hand in a term paper), 'einen Antrag abgeben' (to submit an application), 'Unterlagen abgeben' (to hand in documents), or 'eine Steuererklärung abgeben' (to file a tax return).
Bis wann müssen wir den Antrag für das Stipendium abgeben?
By when do we have to submit the application for the scholarship?
In the meaning 'to emit', the subject is often a technical device or a natural object. It is usually about physical or chemical processes.
Der alte Ofen gibt nicht mehr viel Wärme ab.
The old stove doesn't give off much heat anymore.
In a political context, 'seine Stimme abgeben' (to cast one's vote) is a fixed expression. It is almost always used in this form to describe the act of voting.
Bei der letzten Wahl haben über 70 Prozent der Bürger ihre Stimme abgegeben.
In the last election, over 70 percent of citizens cast their vote.
When you share part of something, the person who receives something is in the dative. The thing being shared often appears with the preposition 'von' (of/from).
Gibst du mir bitte etwas von deiner Schokolade ab?
Will you please share some of your chocolate with me?
When selling or giving something away, 'abgeben' (to sell/give away) is often combined with adverbs like 'günstig' (cheaply), 'billig' (cheaply), or 'kostenlos' (for free).
Er hat seine alten Möbel an Studierende abgegeben.
He gave his old furniture to students.
In a sports context, the ball (accusative object) is passed to a teammate (preposition 'an' + accusative).
Der Stürmer hätte den Ball an seinen Mitspieler abgeben sollen.
The striker should have passed the ball to his teammate.
go / loose
'los' in 'etwas los sein' (to be rid of something) or 'etwas loswerden' (to get rid of something) and 'abgeben' can both have to do with no longer keeping something. 'Los sein' emphasizes the state afterward: the thing is gone. 'Etwas loswerden' emphasizes the wish not to have it anymore. 'Abgeben' describes the action more precisely: you pass something on to a person or place, sometimes for free or at a low price. Learners may confuse the words because you often get rid of something by giving it away. If the handover is important, 'abgeben' fits better; if the feeling of relief is important, 'los' fits better.

Meine Kollegin gibt ihren alten Schreibtisch günstig ab.
My colleague is selling her old desk cheaply.
Nach dem Umzug sind wir viele alte Möbel los.
After the move, we are rid of a lot of old furniture.