türmen
to flee
Colloquial for to flee or run away, often in order to escape an unpleasant situation or punishment.
Als die Polizei kam, ist der Dieb sofort getürmt.
When the police came, the thief fled immediately.

to flee / to pile up
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to flee
Colloquial for to flee or run away, often in order to escape an unpleasant situation or punishment.
Als die Polizei kam, ist der Dieb sofort getürmt.
When the police came, the thief fled immediately.

The verb 'türmen' (to pile up/to flee) is derived from the noun 'der Turm' (tower). The meaning 'to stack something up' is the most literal one. The reflexive form 'sich türmen' describes how something accumulates to a tower-like height.
Die Kinder türmen die Kissen auf dem Sofa.
The children pile up the cushions on the sofa.
The three meanings can be distinguished well grammatically. The colloquial meaning 'fliehen' (to flee) is intransitive. The meaning 'sich anhäufen' (to accumulate) is reflexive ('sich türmen'). The meaning 'aufstapeln' (to stack up) is transitive and needs an accusative object.
Der Einbrecher ist sofort getürmt.
The burglar fled immediately.
In the meaning 'fliehen' (to flee), 'türmen' is a verb of motion. Therefore, the perfect tense is formed with the auxiliary verb 'sein' (to be), not with 'haben' (to have).
Als er das Martinshorn hörte, ist er sofort getürmt.
When he heard the siren, he fled immediately.
Using 'türmen' to mean 'fliehen' (to flee) is clearly colloquial. In formal or written contexts, you would use other verbs.
Kaum hatte ich ihn zur Rede gestellt, ist er getürmt.
No sooner had I confronted him than he took off.
The reflexive form 'sich türmen' (to pile up) is often used for things that accumulate. Typical examples are 'die Arbeit' (work), 'die Schulden' (debts), 'die Probleme' (problems), or 'die Wolken' (clouds).
Am Horizont türmten sich bereits die Gewitterwolken.
Storm clouds were already piling up on the horizon.
to stay / remain
'bleiben' and 'türmen' are opposites here. 'bleiben' means to stay in a place and not leave. 'türmen' is colloquial and means to run away or flee quickly, often because you want to avoid trouble or punishment. 'bleiben' sounds neutral. 'türmen' sounds more casual and fits situations where someone disappears secretly or suddenly. The simple contrast is: someone who 'bleibt' does not leave; someone who 'türmt' runs away.

Als der Lehrer den Test ankündigt, will Paul am liebsten türmen.
When the teacher announces the test, Paul would rather run away.
Wegen des starken Regens bleibt der Kunde noch im Geschäft.
Because of the heavy rain, the customer is staying in the shop a little longer.