In this study, we analyse the aggregated transaction networks of Ether (the native cryptocurrency in Ethereum) and the three most market-capitalised ERC-20 tokens in this platform at the time of writing: Binance, USDT, and Chainlink. We analyse a comprehensive dataset from 2015 to 2020 (encompassing 87,780,546 nodes and 856,207,725 transactions) to understand the mechanism that drives their growth. In a seminal analysis, Kondor et al. (PLoS ONE, 2014, 9: e86197) showed that during its first year, the aggregated Bitcoin transaction network grew following linear preferential attachment. For the Ethereum-based cryptoassets, we find that they present in general super-linear preferential attachment, i.e., the probability for a node to receive a new incoming link is proportional to kα, where k is the node’s degree. Specifically, we find an exponent α = 1.2 for Binance and Chainlink, for Ether α = 1.1, and for USDT α = 1.05. These results reveal that few nodes become hubs rapidly. We then analyse wealth and degree correlation between tokens since many nodes are active simultaneously in different networks. We conclude that, similarly to what happens in Bitcoin, “the rich indeed get richer” in Ethereum and related tokens as well, with wealth much more concentrated than in-degree and out-degree.