Statistics of ideal randomly branched polymers in a semi-space.

We investigate the statistical properties of a randomly branched 3-functional N-link polymer chain without excluded volume, whose one point is fixed at the distance d from the impenetrable surface in a 3-dimensional space. Exactly solving the Dyson-type equation for the partition function Z(N, d )=N(-theta)e(gamma N) in 3D, we find the "surface" critical exponent theta=[Formula: see text], as well as the density profiles of 3-functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.