  We investigate the statistical distribution of transmission eigenvalues in
phase-coherent transport through quantum dots. In two-dimensional ab-initio
simulations for both clean and disordered two-dimensional cavities, we find
markedly different quantum-to-classical crossover scenarios for these two
cases. In particular, we observe the emergence of ``noiseless scattering
states'' in clean cavities, irrespective of sharp-edged entrance and exit lead
mouths. We find the onset of these ''classical'' states to be largely
independent of the cavity's classical chaoticity, but very sensitive with
respect to bulk disorder. Our results suggest that for weakly disordered
cavities the transmission eigenvalue distribution is determined both by
scattering at the disorder potential and the cavity walls. To properly account
for this intermediate parameter regime we introduce a hybrid crossover scheme
which combines previous models that are valid in the ballisic and the
stochastic limit, respectively.
