At a high level, fees are bundled for users of ZetaChain dApps, whether they use cross-chain messaging and/or smart contracts. These fees are distributed to parties providing value to the network in the form of creating transactions, securing the network, or other direct protocol contributions.
Both CCTXs and Smart Contracts have a base fee which is burned (see fee distribution below), and a variable fee. For CCTXs, this is a variable fee proportional to data (kb) sent, while smart contracts have a fee market like EIP 1559. Eventually, CCTXs will transition into a fee market similar to a tip/priority fee structure.
ZetaChain includes a base flat fee of (example) 0.01 ZETA for any transactions, cross-chain messaging transactions or smart contracts. This base fee is adjustable by the network as needed to deal with network traffic and congestion, and is burned.
More details and breakdowns on gas fees involved with Cross-Chain Messaging and Omnichain Smart Contracts will be written.