Disinformation on online social media has been on the rise in the past years. While there is extensive literature modelling social cascades, online disinformation cascades show distinctive characteristics: they provoke debunking reactions, they spread over networks with heterogeneous connectivity, and they compete for the limited attention of users — which recommendation algorithms may partly offset. We propose a model including these ingredients and study it through Monte–Carlo simulations and mean–field approximations, on random graphs and an empirical Twitter network. We find that debunking reactions are double–edged: they reduce the reach of appealing items but allow unappealing ones to reach audiences they would not otherwise reach. Degree heterogeneity makes cascades trigger at a much lower content appeal but limits their final reach: heterogeneous networks are easy to ignite yet hard to saturate. Limited attention cancels the effects from degree heterogeneity, although the mediation of recommendation algorithms may restore them.

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