Hi @tester123 - that's a tall order "call which satisfies in all scenarios or use cases".
If you'll also review the docs on Adobe Analytics then you'll see that some things like link tracking can be set to occur "automatically". However for custom events meaningful to the site being tracked, you'll most likely use a Set Data Values extension to capture the variables you want when the custom event occurs. There's no overall 'fits every situation' rule for this.
Here's an example (image below) where we're setting the actual event (e30) and the other variables we want to capture at that time. It will help to review the Adobe docs on event tracking as well so that you can better understand event tracking. Then at the end is the 'Condition' which informs Tealium when to set these values. In your Adobe tag, the data layer variables have been mapped to populate the Adobe tracking pixel when it fires on the site as the result of a normal pageview, or utag.view() or utag.link() call.
I hope this sample helps - it does take a little time to set this up "the Tealium way" but when you get it working it's satisfying. Some interactive debugger sessions are also helpful for learning exercises.
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