Activation is necessary to form a cloud droplet from an aerosol, and it is widely accepted that it occurs as soon as a wetted aerosol grows beyond its critical radius. Traditional Köhler theory assumes that this growth is driven by the diffusion of water vapor. However, if the wetted aerosols are large enough, the coalescence of two or more particles is an additional process for accumulating sufficient water for activation. This transition from diffusional to collectional growth marks the limit of traditional Köhler theory and it is studied using a Lagrangian cloud model in which aerosols and cloud droplets are represented by individually simulated particles within large-eddy simulations of shallow cumuli. It is shown that the activation of aerosols larger than 0. 1μm in dry radius can be affected by collision and coalescence, and its contribution increases with a power-law relation toward larger radii and becomes the only process for the activation of aerosols larger than 0. 4-0. 8μm depending on aerosol concentration. Due to the natural scarcity of the affected aerosols, the amount of aerosols that are activated by collection is small, with a maximum of 1 in 10000 activations. The fraction increases as the aerosol concentration increases, but decreases again as the number of aerosols becomes too high and the particles too small to cause collections. Moreover, activation by collection is found to affect primarily aerosols that have been entrained above the cloud base.