Abstract The basic concepts of progressive nucleation mechanism are described and the final equations of the mechanism are used to analyze the growth of articles in three randomly selected databases from 20 different databases in humanities (philosopher's index, set 1), social sciences (exceptional child education, set 5) and science and technology (food science and technology, set 10), respectively, covering the period 1968–1987, previously analyzed by Egghe and Ravichandra Rao (1992, Scientometrics 25 (1), 5–46), and the growth of journals, articles and authors in malaria research for the period 1955–2005, reported recently by Ravichandra Rao and Srivastava (2010, Journal of Informetrics 4 (1), 249–256) and compared with the predictions of the power–law equation. Analysis of the former data revealed that: (1) the progressive nucleation mechanism describes the data better than the power–law relation, (2) the field of social sciences is saturated much earlier than science and technology but publication activity in humanities is saturated much later, and (3) that social sciences have the maximum growth, followed by lower growth in humanities and the lowest growth in science and technology. The data on journals J ( t ), papers N ( t ) and authors W ( t ) against publication year Y in malaria research can be described equally well by equations of the power–law and progressive nucleation mechanism, and the growth of journals J ( t ) and articles N ( t ) is intimately connected with the growth of authors W ( t ).