The paper presents an analysis performed over the worldwide top 150 firms in the pharmaceutical industry. It begins with a test of the Gibrat's Law of Proportionate Effect finding, in line with previous literature, a violation concerning the variance of the growth. Then it shows, using disaggregated data on sub-markets (defined according to the ATC code) that this violation can be completely referred to the existence of a ``diversification'' effect, namely a scale relation between the number of active sub-markets a firm posses and its size. The observed scaling property of the firms diversification patterns is in contrast with the linear assumption typically made in literature. Finally, to interpret the findings, the work proposes a stochastic model for firms diversification which fits quite well the data.