  We study the statistical mechanics of RNA secondary structures designed to
have an attraction between two different types of structures as a model system
for heteropolymer aggregation. The competition between the branching entropy of
the secondary structure and the energy gained by pairing drives the RNA to
undergo a `temperature independent' second order phase transition from a molten
to an aggregated phase'. The aggregated phase thus obtained has a
macroscopically large number of contacts between different RNAs. The partition
function scaling exponent for this phase is \theta ~ 1/2 and the crossover
exponent of the phase transition is \nu ~ 5/3. The relevance of these
calculations to the aggregation of biological molecules is discussed.
