| Summary: | The main theme of this thesis is the use of the branching property in the analysis of random structures. The thesis consists of two self-contained parts. In the first part, we study the long-term behaviour of supercritical superdiffusions and prove the strong law of large numbers. The key tools are spine and skeleton decompositions, and the analysis of the corresponding diffusions and branching particle diffusions. In the second part, we consider preferential attachment networks and quantify their vulnerability to targeted attacks. Despite the very involved global topology, locally the network can be approximated by a multitype branching random walk with two killing boundaries. Our arguments exploit this connection.
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