  We present Quantum Monte Carlo calculations with up to N=576000 interacting
bosons in a quasi two-dimensional trap geometry closely related to recent
experiments with atomic gases. The density profile of the gas and the
non-classical moment of inertia yield intrinsic signatures for the
Kosterlitz--Thouless transition temperature T_KT. From the reduced one-body
density matrix, we compute the condensate fraction, which is quite large for
small systems. It decreases slowly with increasing system sizes, vanishing in
the thermodynamic limit. We interpret our data in the framework of the
local-density approximation, and point out the relevance of our results for the
analysis of experiments.
