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The Layer 2 Atomic Cross-Blockchain Function Calls protocol allows composable programming across Ethereum blockchains. It allows for inter-contract and inter-blockchain function calls that are both synchronous and atomic: if one part fails, the whole call graph of function calls is rolled back. Existing atomic cross-blockchain function call protocols are Blockchain Layer 1 protocols, which require changes to the blockchain platform software to operate. Blockchain Layer 2 technologies such as the one described in this paper require no such changes. They operate on top of the infrastructure provided by the blockchain platform software. This paper introduces the protocol and a more scalable variant, provides an initial safety and liveness analysis, and presents the expected overhead of using this technology when compared to using multiple non-atomic single blockchain transactions. The overhead is analysed for three scenarios involving multiple blockchains: the Hotel and Train problem, Supply Chain with Provenance, and an Oracle. The protocol is shown to provide 93.8 or 186 cross-blockchain function calls per second for the Hotel and Train scenario when there are many travel agencies, for the standard and scalable variant of the protocol respectively, given the Ethereum client, Hyperledger Besu's performance of 375 tps, assuming a block period of one second, and assuming all transactions take the same amount of time to execute as the benchmark transactions.