  We analyze simple models of quantum chaotic scattering, namely quantized open
baker's maps. We numerically compute the density of quantum resonances in the
semiclassical r\'{e}gime. This density satisfies a fractal Weyl law, where the
exponent is governed by the (fractal) dimension of the set of trapped
trajectories. This type of behaviour is also expected in the (physically more
relevant) case of Hamiltonian chaotic scattering. Within a simplified model, we
are able to rigorously prove this Weyl law, and compute quantities related to
the "coherent transport" through the system, namely the conductance and "shot
noise". The latter is close to the prediction of random matrix theory.
