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Network meta-analysis (NMA) is widely used in evidence synthesis to estimate the effects of several competing interventions for a given clinical condition. One of the challenges is that it is not possible in disconnected networks. Component network meta-analysis (CNMA) allows technically 'reconnecting' a disconnected network with multicomponent interventions. The additive CNMA model assumes that the effect of any multicomponent intervention is the additive sum of its components. This assumption can be relaxed by adding interaction component terms, which improves the goodness of fit but decreases the network connectivity. Model selection aims at finding the model with a reasonable balance between the goodness of fit and connectivity (selected CNMA model). We aim to introduce a forward model selection strategy for CNMA models and to investigate the performance of CNMA models for connected and disconnected networks. We applied the methods to a real Cochrane review dataset and simulated data with additive, mildly, or strongly violated intervention effects. We started with connected networks, and we artificially constructed disconnected networks. We compared the results of the additive and the selected CNMAs from each connected and disconnected network with the NMA using the mean squared error and coverage probability. CNMA models provide good performance for connected networks and can be an alternative to standard NMA if additivity holds. On the contrary, model selection does not perform well for disconnected networks, and we recommend conducting separate analyses of subnetworks.