Seed-mediated methods are widely used in industrial or academic laboratories for the synthesis of nanoparticles of controlled shape and size. In the natural medium, precipitation of secondary minerals also often take place on seeds. In this context, we have devised a formalism which accounts for the competition between seed growth and nucleation and growth of secondary particles in an initially over-saturated aqueous solution. Based on the classical nucleation theory, it involves a size-dependent growth law which accounts for Ostwald ripening effects, unlike most water-rock interaction codes. We find that, in such closed system, seed growth and nucleation/growth of secondary particles are strongly coupled. In the multi-dimensional parameter space, regions where one or the other process prevails are well-separated by a rather abrupt transition. In general, the value of the initial seed total surface area is insufficient to fully orientate the synthesis. Relying on this approach, we propose an alternative interpretation of recent experimental results on amorphous silica nanoparticle synthesis. Besides fundamental understanding of the kinetics of precipitation, the interest of the present approach is to serve as a guideline to experimentalists or industrialists working in seed-mediated syntheses and warn on the undesired formation of secondary particles when monodispersed distributions of nano-or micro-particles are searched.