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Cirrus ice crystals are produced heterogeneously on ice‐nucleating particles (INPs) and homogeneously in supercooled liquid solution droplets. They grow by uptake of water molecules from the ice‐supersaturated vapor. The precursor particles, characterized by disparate ice nucleation abilities and number concentrations, compete for available vapor during ice formation events. We investigate cirrus formation events systematically in different temperature and updraft regimes, and for different INP number concentrations and time‐independent nucleation efficiencies. We consider vertical air motion variability due to mesoscale gravity waves and effects of supersaturation‐dependent deposition coefficients for water molecules on ice surfaces. We analyze ice crystal properties to better understand the dynamics of competing nucleation processes. We study the reduction of ice crystal numbers produced by homogeneous freezing due to INPs in both, individual simulations assuming constant updraft speeds and in ensemble simulations based on a stochastic representation of vertical wind speed fluctuations. We simulate and interpret probability distributions of total nucleated ice crystal number concentrations, showing signatures of homogeneous and heterogeneous nucleation. At typically observed, mean updraft speeds (≈15 cm s⁻¹) competing nucleation should occur frequently, even at rather low INP number concentrations (<10 L⁻¹). INPs increase cirrus occurrence and may alter cirrus microphysical properties without entirely suppressing homogeneous freezing events. We suggest to improve ice growth models, especially for low cirrus temperatures (<220 K) and low ice supersaturation (<0.3).