Theoretically, the TON blockchain can process over 15,000+ transactions per second and more, thanks to its high transaction throughput design and potential to scale to millions of transactions per second through multi-chain support for scalability.

The TON network enables sharding based on the ChainID naturally, with a large number of workchains available for use, as described in the Parameters that validators are running. You can check the following link for more details: https://ton.org/docs/learn/overviews/addresses#workchain-id-account-id

However, the current maximum bandwidth of the system is limited by the existing infrastructure and the number of validators in the network. As of the knowledge cutoff date of September 2021, the TON blockchain was reportedly capable of processing up to 15,000 transactions per second (TPS) with a target confirmation time of 5 seconds.

It's important to note that this number may have changed since then and can vary depending on network conditions and other factors. Moreover, the TON blockchain is continually being optimized and enhanced, so it's possible that the maximum throughput may increase in the future as the network continues to grow and evolve.

The network config paramters in details:
https://ton.org/docs/develop/howto/network-configs