@Frish - to add to @ruipedromachado's post, there's another important consideration when looking to move tags from the client-side to the server-side - cookies.
Often, simple web-based trackers like the ones in Rui's post rely on 3rd party cookies to transmit meaningful data to the vendor in question, and/or set user-level identification cookies in the request response (with a Set-Cookie header).
Without that user-level information, those outgoing requests wouldn't be useful (because the vendor wouldn't know which user has viewed that page, or which click to associate with the conversion, etc).
That's why Tealium offers a number of Cookie Sync tags and related functionalities. Those vendor-specific tags retrieve/create such cookies and allow the values to be persisted on Tealium's side so they can be sent to the vendor manually from our servers. This example for Criteo and this one for TheTradeDesk have a bit more detail about the approach in AudienceStream (where you can persist that data on the Visitor Profile), and we've documented it more generally for EventStream as well (where we use our own third-party cookie to persist that data, since EventStream is event- (not profile-) driven.
Long story short, it's not quite as simple as just moving the tag, you also need to find out what additional information is generally delivered via 3rd party cookie to that vendor in their web-based solutuion, and find out if the vendors offers a way to retrieve it so that it can be persisted in Tealium and sent to the vendor accordingly.
Hope that helps?
Best, Caleb
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