The specific operation method of distributing goods with one click on mobile Taobao without a source of goods may vary depending on the merchant's backend system, but the general steps are as follows:

1. Log in to your Taobao account: Use your Taobao account to log in to mobile Taobao.

2. Enter the merchant's backend: Click "My Taobao", then click "Merchant Center" or "Qianniu Workbench" to enter the merchant's backend.

3. Enter the product management interface: Find relevant options such as "Product Management" or "Product Release" in the merchant's backend to enter the product management interface.

4. Select the source of the product: In the product management interface, you need to select the source of the product you want to distribute with one click. This may be a product that the merchant already has, or a product from other platforms (such as 1688, etc.).

5. Use the one-click distribution tool: Taobao provides a one-click distribution tool, which you can find in the product management interface. The one-click distribution tool can help you quickly copy products from other platforms to Taobao stores, and automatically complete the modification and release of product information.

6. Confirm the distribution information: When using the one-click distribution tool, please carefully check the distribution information, such as price, inventory, etc., to ensure that it is consistent with the original product. If necessary, please modify the distribution information according to the actual situation.

7. Release the product: After confirming that the distribution information is correct, click the "Release Product" or "Release Now" button to complete the one-click distribution operation.

Please note that the one-click distribution tool may require payment, and the specific price and functions may vary depending on the merchant's backend. When using the one-click distribution tool, please make sure to comply with Taobao's relevant regulations and policies. I wish you success in operating your Taobao store!