Does QB on line (desktop version) automatically update? How do I know whether I have the latest version? the sign on screen says I have version 3.5.2

Let's identify what version you're using and check for updates for your QuickBooks Online desktop app, Rabbit1.

To check the current version and release details, open the QuickBooks Online Desktop App and press the F2 key on your keyboard to view the version and release information.

Alternatively, you can navigate to the Help menu and select About QuickBooks to view the app version details.
 

If you don't have the updated version yet, please refer to this resource article for downloading it. This article provides the latest executable (.exe) file for the most recent release of the QuickBooks Online desktop app: Download and use the QuickBooks app on your computer.

Regarding your question about auto-updates, the QuickBooks Online desktop app will automatically update as long as your Windows system settings have automatic updates enabled.

If you have any further questions or need assistance with other QuickBooks tasks, feel free to reply here or start a new post in this forum.