  Quantum point contact devices are indispensable tools for probing the edge
structure of the fractional quantum Hall (FQH) states. Recent observations of
quantized conductance plateaus accompanied by shot noise in such devices, as
well as suppression of Mach-Zehnder interference, call for theoretical
explanations. In this paper, we develop a theory of FQH edge state transport
through quantum point contacts, which allows for a generic Abelian edge
structure and assumes strong equilibration between edge modes (incoherent
transport regime). We find that conductance plateaus are found whenever the
quantum point contact locally depletes the Hall bar to a stable region with a
filling factor lower than that of the bulk and the resulting edge states
equilibrate. The shot noise generated on these plateaus can be classified
according to 13 possible combinations of edge charge and heat transport in the
device. We also comment on a relation between the the emergence of quantized
plateaus and the suppression of Mach-Zehnder interference. Besides explaining
recent experimental findings, our results provide novel insights and
perspectives on quantum point contact devices in the FQH regime.
