hinüber
across
Expresses movement to the other side of something, away from the speaker.
Kommst du kurz zu mir hinüber?
Are you coming over to me for a moment?

across / broken / gone
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across
Expresses movement to the other side of something, away from the speaker.
Kommst du kurz zu mir hinüber?
Are you coming over to me for a moment?

The adverb 'hinüber' consists of 'hin' and 'über'. The prefix 'hin' describes movement away from the speaker, while 'über' indicates movement over a boundary or to the other side.
Siehst du den Kiosk dort? Ich gehe mal kurz hinüber und kaufe eine Zeitung.
Do you see the kiosk over there? I'll just go across and buy a newspaper.
The literal meaning (movement) is almost always used with a verb of motion such as 'gehen' (to go), 'fahren' (to drive), or 'schauen' (to look). The colloquial meanings 'kaputt' (broken) or 'tot' (dead), on the other hand, almost always appear with the verb 'sein' (to be).
Er schwamm schnell zum anderen Ufer hinüber.
He quickly swam across to the other bank.
In the meaning 'kaputt' (broken), 'hinüber' is very colloquial. In formal or written contexts, other expressions would be used.
Lass das Glas nicht fallen, sonst ist es hinüber!
Don't drop the glass, or it'll be broken!
The use of 'hinüber' for 'gestorben' (died) is a euphemism. That means it is a gentler, indirect way of referring to an unpleasant topic.
Der alte Hund meiner Nachbarin ist letzte Woche ganz friedlich hinüber.
My neighbor's old dog passed away very peacefully last week.
over / about
'über' and 'hinüber' can both have to do with movement to the other side. 'über' is a preposition and normally needs a noun: you go 'über die Straße' (across the street) or 'über die Brücke' (over/across the bridge). 'hinüber' is an adverb and names the direction: to the other side, usually away from the speaker. So you say 'geh hinüber' (go over there) when it is clear where to or which other side is meant. Learners may confuse the words because both describe movement across a boundary or surface. The important point is: 'über' names the path or surface, while 'hinüber' names the direction to the other side.

Die Nachbarin winkt vom Garten und kommt gleich hinüber.
The neighbor waves from the garden and is coming over in a moment.
Nach dem Essen geht Paul über die Straße zur Apotheke.
After eating, Paul goes across the street to the pharmacy.