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.

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.
full
'voll' and 'überlaufen' can both mean that there is no space left. 'voll' is more general and fits bags, glasses, rooms, or places with many people. 'überlaufen' is stronger and often has a negative effect: a place is visited by too many people, or a liquid really flows over the edge. With crowds, 'überlaufen' suggests something more like: it is unpleasantly crowded. With liquids, 'überlaufen' describes a movement, not just a state.

Im Sommer ist der Strand oft überlaufen, deshalb fahren wir lieber früh am Morgen hin.
In summer, the beach is often overcrowded, so we prefer to go there early in the morning.
Am Samstag war der Bus so voll, dass Lukas stehen musste.
On Saturday, the bus was so full that Lukas had to stand.