Had a new one today with a wet runway. The B737 ahead of us started its takeoff roll as we took the turn to the holding area. We never stopped more than a few secs before turning onto the active runway in a rolling takeoff. As we were just finishing the turn while accelerating I looked down the runway and the B737 was still throwing up rain water probably between V1 and lift off. I judged if the first plane was to abort and remain on the ground we would overfly it. This concerned me somewhat even thou it turned out to be nothing. I suspect that the judgement was either by the ATC clearance or a misunderstanding by our crew.

I'm confused. The holding area?

I think what happened is ATC clears AC1 to takeoff.
While AC1 is rolling, ATC instructs your flight (AC2) to enter the runway (position and hold). Once ATC sees AC1 wheels lift off runway, they clear AC2 for takeoff.

Is it possible ATC messed up and told AC2 to takeoff before AC1 had wheels off ground? Yes. Is it possible AC2 expecting clearance to takeoff, took off despite only being told to position and hold? Yes. However it's very likely that from your vantage point and w/o benefit of ATC, you simply saw what looked like, but wasn't a violation.

Give us the flight number and we can listen to it on Live ATC.

Well you should watch some videos of military aircraft doing minimum interval takeoffs (as close as 12 seconds apart). But I doubt this was unsafe. Your crew may well have been anticipating getting clearance as I’ve had flights where we turned onto the runway and continued to roll (not come to a complete stop) before the throttles were fully advanced to takeoff thrust. While the crew on your flight may well have advanced the throttles somewhat as they were turning on to the runway they likely (almost certainly) didn’t apply takeoff thrust until getting clearance from ATC to takeoff. You may well have heard the engines spool up but not necessarily to takeoff thrust. Applying takeoff thrust is a two step process in which first the throttle is advanced slightly before takeoff thrust is set to reduce any impacts of potential asymmetric thrust if the engines don’t spool up simultaneously, even when all throttle levers are advanced at the same time.

This article from Airbus explains the two step process of advancing the throttle for takeoff and why its a two-step profess.
https://safetyfirst.airbus.com/engin...ng-at-takeoff/

This is known as "Anticipated Separation" and it's completely normal. In fact airport's like ATL, ORD, and JFK couldn't operate if Tower controllers didn't use this procedure

Yep, seen this quite a bit at ATL. As long as weather conditions aren't conducive for above-average wake [turbulence] persistence, this is perfectly normal.

Funny enough, I've actually seen this more when it's a wet runway than not, but I'm sure that's an observation bias.

Exactly, and don�t forget, at the point that the OP saw AC1, it was likely 5000� down the runway at 150kts while the OP was basically stopped. That mile separation only grows larger as AC1 continues to lift off and accelerate and eventual turn off the runway heading.

your horizontal separation was always a mile or more at the closest point.

Great answers putting this in perspective. I had considere all this but but just wanted comments to calm me down. My wife gets upset when I make whispered comments in flight like "boy that was close" She still tells all her friends about the time I told her "we're going off the runway" when the engines started spitting sparks out the front and making booming noises during a long landing?

Yup,I would like to know what was said on the ATC but I don't want to identify a specific on a public forum when it's so minor in most people's minds. I'll be glad to privately supply the fight number if it would be a learning process

are you sure you�re in the right thread?

In addition to what everyone else has said, there is nothing that requires ATC to have the plane lined up waiting at a complete stop on the runway prior to receiving takeoff clearance. If there is enough separation, they can clear the flight for takeoff while you're approaching the runway from the taxiway, which is why you might roll directly onto the runway and take off without ever coming to a stop on the runway (most frequently experienced this when there was minimal departure traffic and no arrival traffic on the same runway). Or you don't know how much time passed between ATC clearing the plane onto the runway to line up vs clearing it to takeoff. As someone who frequently listens to ATC while departing, it's not uncommon that when Plane A is given takeoff clearance, Plane B is almost simultaneously told to "line up and wait", and as soon as plane A will achieve the necessary separation plane B gets their takeoff instructions. Without having the ATC feed you don't know how much time passed between those instructions and your pilots responding to those instructions. For example say plane B is told to line up and wait, it takes 20 seconds before they actually start moving onto the runway, at which point plane A may have achieved adequate separation, so they can clear plane B for takeoff even though they never finished lining up/came to complete stop.

As above though, really just need to ATC feed going to know what was actually said and match it to what your flight is doing. "{AIRPORT CODE} ATC LIVE" is what I usually google to find it. Ground will get you from the gate to the taxiway prior to the runway, Tower will get you the transmissions regarding runway activity

Remember that the airplane has windows in the cockpit. The pilots can see the preceding aircraft and aren't going to takeoff if he hasn't lifted off.

Note, also, that he said between V1 and takeoff. If the plane in front has passed V1 it would take something pretty catastrophic for it not to take off. (On the other hand, there is that video, I think from a former Russian republic, where a pilot rejected a takeoff after V1. He deliberately crashed the plane and immediately punched out. It was the right choice--better to crash into the runway than the apartment building he would otherwise have hit.)

He said "probably" between V1 and takeoff. No way to know unless you were in that cockpit.

The takeoff clearance was based on the "anticipated separation" standard mentioned above and, likely, diverging headings once airborne. The crew can see the airplane taking off in front of them and aren't going to continue the takeoff if there isn't enough room. It's also trivial to reject a takeoff at low (<80 kts) speed if the previous airplane doesn't takeoff.

We don�t take off when another aircraft is on the same runway. Ever.