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We consider two types of random networks grown in blocks. Hooking networksare grown from a set of graphs as blocks, each with a labelled vertex called ahook. At each step in the growth of the network, a vertex called a latch ischosen from the hooking network and a copy of one of the blocks is attached byfusing its hook with the latch. Bipolar networks are grown from a set ofdirected graphs as blocks, each with a single source and a single sink. At eachstep in the growth of the network, an arc is chosen and is replaced with a copyof one of the blocks. Using P\'olya urns, we prove normal limit laws for thedegree distributions of both networks. We extend previous results by allowingfor more than one block in the growth of the networks and by studyingarbitrarily large degrees.

Normal limit laws for vertex degrees in randomly grown hooking networks and bipolar networks