vielerorts
in many places
In many different places; in numerous areas.
Nach den starken Regenfällen kam es vielerorts zu Überschwemmungen.
After the heavy rainfall, flooding occurred in many places.

in many places
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in many places
In many different places; in numerous areas.
Nach den starken Regenfällen kam es vielerorts zu Überschwemmungen.
After the heavy rainfall, flooding occurred in many places.

'Vielerorts' (in many places) is an old genitive form. It is made up of 'vieler' (genitive plural of 'viele') and 'Orts' (genitive singular of 'der Ort'). Literally, it therefore means 'in many places.'
Die Tradition wird heute noch vielerorts gepflegt.
The tradition is still maintained in many places today.
As an adverb, 'vielerorts' (in many places) can be placed flexibly in a sentence. It can be in position 1, in which case the verb follows directly after it. But it can also appear after the verb and the subject in the middle of the sentence.
Vielerorts fielen die Schulen wegen des Schnees aus.
In many places, schools were closed because of the snow.
This word belongs more to written language or a more formal style. You often find it in news reports, articles, or official announcements.
Wie die Polizei mitteilte, kam es vielerorts zu Verkehrsbehinderungen.
According to the police, traffic disruptions occurred in many places.
everywhere
'überall' and 'vielerorts' both say that something occurs in several places. The important difference is the amount: 'überall' really means in all places or at every spot. 'vielerorts' means only in many places, but not necessarily in all of them. Learners may confuse the words because both express wide distribution. 'überall' sounds very natural in everyday language. 'vielerorts' sounds a bit more factual and works well in news, weather, or general reports.

Vielerorts fallen heute wegen des Sturms die Züge aus.
In many places, trains are canceled today because of the storm.
Im Park blühen überall kleine gelbe Blumen.
Small yellow flowers are blooming everywhere in the park.