<p><strong>Abstract.</strong> The modern parametrization of the classical theory of nucleation (κ-Kӧhler theory) implicitly assumes a Dirac delta distribution to model the density of ideal spherical point size dry particles and droplets. However, anthropogenic activities like combustion or other high temperature processes frequently result in the emission of aerosols in the form of polydisperse fractal-like aggregates composed of condensed phase nanoparticles (for instance soot). If certain conditions are met, the emitted particles are known to evolve into important cloud condensation nuclei (CCN) in the atmosphere, however their behavior as CCN can deviate significantly from theoretical predictions. In this work, an extension of κ-Kӧhler theory is proposed that takes into account the effect of the size distribution and particle morphology on the activation of the aerosol dry particles. A theoretical and experimental approach are combined to derive the dependence of the activated fraction on supersaturation <i>F</i>_a&amp;thinsp;=&amp;thinsp;<i>F</i>_a(<i>SS</i>) on parameters that describe the size distribution and morphology of the particles like the geometric standard deviation and the fractal dimension of the aggregates. The model is tested on two different aerosols, a simple case of isolated quasi-spherical ammonium sulfate particles generated by atomization, and complex morphology soot aggregates generated by a laboratory diffusion jet flame.</p>