  We consider a quasilinear equation involving the $n-$Laplacian and an
exponential nonlinearity, a problem that includes the celebrated Liouville
equation in the plane as a special case. For a non-compact sequence of
solutions it is known that the exponential nonlinearity converges, up to a
subsequence, to a sum of Dirac measures. By performing a precise local
asymptotic analysis we complete such a result by showing that the corresponding
Dirac masses are quantized as multiples of a given one, related to the mass of
limiting profiles after rescaling according to the classification result
obtained by the first author in P. Esposito, A classification result for the
quasi-linear Liouville equation. Ann. Inst. H. Poincar\'e Anal. Non Lin\`eaire
35 (2018), no. 3, 781--801. A fundamental tool is provided here by some Harnack
inequality of "sup+inf" type, a question of independent interest that we prove
in the quasilinear context through a new and simple blow-up approach.
