  Percolation clusters are random fractals whose geometrical and transport
properties can be characterized with the help of probability distribution
functions. Using renormalized field theory, we determine the asymptotic form of
various of such distribution functions in the limits where certain scaling
variables become small or large. Our study includes the pair-connection
probability, the distributions of the fractal masses of the backbone, the red
bonds and the shortest, the longest and the average self-avoiding walk between
any two points on a cluster, as well as the distribution of the total
resistance in the random resistor network. Our analysis draws solely on
general, structural features of the underlying diagrammatic perturbation
theory, and hence our main results are valid to arbitrary loop order.
