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We propose a model for cell polarization based on the Becker-D\"oringequations with the first coagulation coefficient equal to zero. We showconvergence to equilibrium for power-law coagulation and fragmentation ratesand obtain a loss of mass in the limit $t \rightarrow \infty$ depending on theinitial mass and the relative strengths of the coagulation and fragmentationprocesses. In the case of linear rates, we further show that large clustersevolve in a self-similar manner at large times by comparing limits ofappropriately rescaled solutions in different spaces.

A Becker-D\"oring type model for cell polarization