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While trying to do some reading for the question Need help understanding staging shown in infographic of Titan launch of Hexagon satellites I ran across the Wikipedia article for Titan III.

This article mentions "Stage 0"

Is the usage of "Stage 0" specific to Titan IIIC or was it in more widespread use at the time?

Does a "Stage 0" complete it's burn and separate before Stage 1 ignites? What makes a booster a proper "Stage 0"?

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    $\begingroup$ I've seen stage 0 refer to strap-on boosters. In that usage, the space shuttle SRBs would be termed "stage 0" and the orbiter itself would be stage 1 (not that I've ever seen this sort of terminology applied to the space shuttle). I've also seen stage 0 applied to the carrier aircraft in an air-launch system e.g. the Pegasus, again, not that I've actually seen it applied to the Pegasus. I think the common thread is that stage 1 is the first stage of the rocket proper, and stage 0 is either an auxiliary booster (started concurrently with stage 1) or is a non-rocket. $\endgroup$ – Anthony X Oct 2 at 0:50
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Partial answer - don't know how to answer the "how often" part.

It's a historical artifact - they had years of Titan documents, procedures, display and controls, etc referring to the "first stage" and the "second stage." They're not going to go back and change all that because somebody had the bright idea of airstarting it. Nope, we'll just call the boosters "stage zero".

The Titan first stage ignited just prior to SRM separation:

Titan Stage I ignition occurs at approximately 112 seconds after liftoff. The actual time is controlled by three majority-voted acceleration switches which command ignition and initiate a staging timer when vehicle acceleration reduces to 1.5 g. Approximately 12 seconds later the SRMs are jettisoned upon command from the staging timer.

From section 2.4 TITAN/CENTAUR FLIGHT SEQUENCE in Source

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