The component was not designed with the intention of filling up the entire screen with alerts. There is no method that returns the number of currently open alerts, but the Show method returns an UltraDesktopAlertWindowInfo instance that provides information about the window that was shown, and you can pass such an instance to the component's IsOpen method to determine whether it is still open. If you add each of these instances to a list when you call the show method, iterate that list and call the IsOpen method on each member, you can get a count on the current open alerts. Also, since the UltraDesktopAlertWindowInfo class exposes a Bounds property, from which you can get the alert's screen location and size, you should also be able to determine when the screen is filled up by using the union of those rectangles.

The fact that the component allows this to happen could be considered a bug, so you might want to log an incident. The solution would probably be a property that dictates the maximum number of the alerts that can be open, with an exception being thrown when that number is exceeded.