In AEM Cloud Service, content is published using Sling Content Distribution to move the content to replicate to a pipeline service run on Adobe I/O that is outside of the AEM runtime.
The replication agents used in previous versions of AEM are no longer used or provided. You can check [0] for more details.
[0]: https://docs.adobe.com/content/help/en/experience-manager-cloud-service/operations/replication.html
Methods of Publishing Content
Quick Un/Publish - Planned Un/Publish
These standard AEM functionalities for the authors do not change with AEM Cloud Service.
Tree Activation
To perform a tree activation:
From the AEM Start Menu navigate to Tools > Deployment > Distribution
Select the card forwardPublisher
Once in the forwardPublisher Web console UI,
select Distribute 
Select the path in the path browser, choose to add a node, tree or delete as required and select Submit