
überlaufen
overcrowded
Visited by or filled with very many people, often more than is pleasant.
Der Strand war am Wochenende völlig überlaufen.
The beach was completely overcrowded on the weekend.
to overflow / to defect / overcrowded
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overcrowded
Visited by or filled with very many people, often more than is pleasant.
Der Strand war am Wochenende völlig überlaufen.
The beach was completely overcrowded on the weekend.

to overflow
To be so full that a liquid flows over the edge.
Die Badewanne ist übergelaufen, weil niemand den Hahn zugedreht hat.
The bathtub overflowed because no one turned off the tap.

to defect to
To leave one's own side, such as an army or party, and join the opponent.
Der Spion ist vor Jahren zum Feind übergelaufen.
The spy defected to the enemy years ago.
The grammar of 'überlaufen' depends on the meaning. When a liquid overflows or a person changes sides, the verb is separable (läuft über, ist übergelaufen). In the meaning 'überfüllt' (overcrowded), the inseparable past participle form 'überlaufen' is used like an adjective.
Pass auf, die Milch kocht gleich über!
Watch out, the milk is about to boil over!
You can recognize the meaning from the subject. If the subject is a place (city, square), it is overcrowded. If it is a liquid (milk, water), it overflows. If it is a person (soldier, spy), they change sides.
Die Altstadt ist an Samstagen oft überlaufen.
The old town is often overcrowded on Saturdays.
In the meaning 'überfüllt' (overcrowded), the past participle form 'überlaufen' is almost always used, either as an adjective before a noun or with the verb 'sein' (to be).
Wir suchen uns ein Café, das nicht so überlaufen ist.
Let's find a café that isn't so overcrowded.
When a person changes sides, the preposition 'zu' with the dative is always used to indicate the destination.
Der Politiker ist zu einer anderen Partei übergelaufen.
The politician defected to another party.
overcrowded
überfüllt and überlaufen can both describe an unpleasantly crowded place. überfüllt emphasizes that there is hardly any space left. überlaufen, on the other hand, highlights the very large number of visitors, without necessarily referring to specific physical crampedness.

Der beliebte Stadtstrand ist im Sommer oft überlaufen, weil täglich sehr viele Gäste kommen.
The popular city beach is often overrun in summer because very many visitors come every day.
Der kleine Stadtstrand ist heute überfüllt, sodass kaum noch Platz für ein Handtuch bleibt.
The small city beach is overcrowded today, leaving hardly any room for a towel.