When logged into ZED, visit the the activity page by clicking on the activity icon which is located next to your stable icon in the top right hand corner of your screen. In the activity page, you can view a list of all your transactions along with the associated transaction hash/ID (i.e. smart contract).
All transactions made in ZED such as buying, selling, breeding and racing outcomes will be tied to a transaction hash/ID on the blockchain that can be traced by using Etherscan, giving you comfort and security over ownership and the transfer of Ether.
The transaction hash/ID in your stable and activity is a clickable link that will redirect you to Etherscan showing your transaction on the blockchain.