  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 $\theta={5/2}$, 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.
