Dendritic molecules are highly-branched arborescent structures and have found applications as chemical reagents, lubricants, contrast media for magnetic resonance, and others. Dendritic nucleic acids could be extremely useful for the development of nucleic acid diagnostics as signal amplification tools and potentially as drug (antisense) delivery vehicles. Further, due to the relatively large size of nucleic acid molecules, nucleic acid dendrimers could be readily labeled with numerous fluorescent compounds and/or protein moieties with limited steric hindrance and/or quenching. Herein, we present a physical-mathematical model of a new class of dendrimers, constructed entirely from unique nucleic acid monomers that are designed such that sequential hybridization adds successive layers of monomer in a geometric expansion of both mass and free single-stranded sequences, called arms, at the surface. The specially designed monomer is a heterodimer of two single-stranded nucleic acid oligomers possessing a central double-stranded waist and four single-stranded arms for binding. Assembly of a dendrimer is initiated from a single monomer and proceeds in layers, the first comprising four monomers, which provides 12 single-stranded arms. Thus, the second layer adds 12 monomers resulting in 36 single-stranded arms. After addition of the 6th layer, the dendrimer is comprised of 1457 monomers, of which 972 reside in the 6th layer, which possesses 2916 single-stranded arms. The accompanying mathematical description of a dendrimer's growth is generic. A natural consequence and limiting condition of the growth process we describe is a saturated solution of nucleic acid, which is, in effect, a "nucleic acid membrane".