When publishing with a New Contract, the publish flow will typically include two transactions:

When publishing, simply reject the second transaction to mint a token.

First, select a create flow with the spec you're looking to deploy(ERC721 or ERC1155). In this example we'll deploy an ERC721 Contract. We'll start by clicking 1 of 1.

Now let's select + New Contract

Stage the contract as you'd like it to appear on Etherscan.

Next, stage the token. Please note, this token won't be published. Feel free to use dummy data.

Once the token is staged, follow the steps until you're ready to publish.

Once you click publish, you'll see a pop-up with several steps.

First, let the token Asset upload.

Next, when it comes to deploy the contract, click the 'Confirm' button after you've reviewed it.

🎉 Once this step is completed your contract is now deployed! 🎉

To deploy only the contract, you'll reject the transaction in the third step.