Solutions of the poly(propylene imine) dendrimers DAB-dendr-(PA)(32) and DAB-dendr-(PA)(64) in methanol are investigated with small angle neutron scattering over the range of dendrimer mass fraction 0.01 less than or equal to x less than or equal to 0.80. The single particle scattering function, P(q), is used to calculate the structure factor, S(q) of the dendrimer solutions and to evaluate the radius of gyration of the dendrimers in dilute solution giving R-g(+)(DAB-dendr-(PA)(32)) = 12.4 +/- 0.2 Angstrom and R-g(+)(DAB-dendr-(PA)(64)) = (15.6 +/- 0.2) Angstrom. In each case the segment density in dilute solution is 0.35 +/- 0.03 g cm(-3), leaving a large fraction of the dendrimer volume accessible to solvent. We define the "dilute solution regime" for dendrimers to extend to a concentration where the swollen dendrimer volume fraction first equals the value 0.64, which comes at a dendrimer weight fraction of x = 0.25. At this concentration, the spatial arrangement of the dendrimers can be described as a random close packing. For higher concentrations, the experimental scattering functions appear to be self-similar up to a mass fraction of x approximate to 0.60. These observations are consistent with a model of concentrated dendrimer solutions which assumes that individual dendrimers collapse to maintain a volume fraction phi approximate to 0.64, which is the volume fraction of random close packing of hard spheres. Preliminary small X-ray scattering data give further evidence of the dendrimer collapse.