The past two decades have seen significant successes in our understanding of networked systems, from the mapping of real-world networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions and provide limited insight into higher-order structures. Such multi-component interactions can only be grasped through simplicial complexes, which have recently found applications in social, technological and biological contexts. Here we introduce, study, and characterize a model to grow simplicial complexes of order two, i.e. nodes, links and triangles. Specifically, through a combination of preferential and/or non preferential attachment mechanisms, the model constructs networks with a scale-free degree distribution and an either bounded or scale-free generalized degree distribution. Allowing to analytically control the scaling exponents we arrive at a highly general scheme by which one is able to construct ensembles of synthetic complexes displaying desired statistical properties.