  The multiplex network growth literature has been confined to homogeneous
growth hitherto, where the number of links that each new incoming node
establishes is the same across layers. This paper focuses on heterogeneous
growth. We first analyze the case of two preferentially growing layers and find
a closed-form expression for the inter-layer degree distribution, and
demonstrate that non-trivial inter-layer degree correlations emerge in the
steady state. Then we focus on the case of uniform growth. Surprisingly,
inter-layer correlations arise in the random case, too. Also, we observe that
the expression for the average layer-2 degree of nodes whose layer-1 degree is
k, is identical for the uniform and preferential schemes. Throughout,
theoretical predictions are corroborated using Monte Carlo simulations.
