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In this work we determine the expected number of vertices of degree k = k(n) in a graph with n vertices that is drawn uniformly at random from a subcritical graph class. Examples of such classes are outerplanar, series-parallel, cactus and clique graphs. Moreover, we provide exponentially small bounds for the probability that the quantities in question deviate from their expected values. † Parts of this work appeared as an extended abstract in N. Bernasconi, K. Panagiotou and A. Steger, 'On thedoi:10.1017/s0963548309990368 fatcat:liahgjzflbh5tmxk5t4bjxtppa