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Component sizes in the usual random graph process are a special case of the Marcus]Lushnikov process discussed in the scientific literature, so it is natural to ask how theory surrounding emergence of the giant component generalizes to the Marcus] Lushnikov process. Essentially no rigorous results are known; we make a start by proving a weak result, but our main purpose is to draw this topic to the attention of random graph theorists. Q 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 179]196, 1998

Emergence of the giant component in special Marcus-Lushnikov processes