Are German universities overcrowded ?

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Ya, unfortunately yes!
Because of the governments decision to make education free in 2012 gave rise to this trend and it was latter revamped by abolishing compulsory military or civil service for the German citizens. Abolishing tuition fees acted as student pullers not only among EU nations but also with Asia and Americas.

But the good news for foreign students is not all the English taught courses are overcrowded. Of course even these courses are running with almost full capacity from the past two years. If the same situation prevails they could also follow the same suit.