Quoted:
Does a car's ECU adjust to a new component gradually?

My car has been intermittently running rough for a while and having eliminated fuel problems without fully solving it I changed the coil pack and it was immediately fixed. Great, bu I noticed it seems to run more smoothly with time/use. Does the ECU take time to adjust to new parameters.............?

Quoted:
Possibly, dependent on age of car, adaptation will take place.

All Bosch OBD1 DME from 3.3 circa 92 have the ability to learn when used in conjunction with Hot wire mass metering unit & throttle position sensor as opposed
to to 2 position throttle switch  which gives two fuelling conditions above 0.5 volts idle position, ie part throttle closed loop fuelling & wide open throttle.
This covers lean side of Lambda @ 1 to 1.1 &  & enriched wide open throttle condition @ 0.8-0.9.

OBD 2 cars circa 98-99 on with more emission focused DME from Bosch, Siemans & Marelli etc run a very tight emission control with misfire detection.
To fuel correctly, this era of engine needs to measure volume of air & its temp, Position of crank & camshafts relative to each other to trigger fuel & water temp
primarily but oil temp can also be used to limit engine rpm from cold start. These later EOBD2 systems will have electronic throttle with integrated idle control valve
so throttle position is also measured via potentiometers.
After combustion condition is measured by one or two oxygen sensors so any overfuelling detected here will force the engine to retard the ignition & possible reduced operation. ( misfires often cause this due to fuel mixture not being fully combusted. Raw fuel ignition at the front of the catalyst monlith will drive high exhaust temps & can weld the front of the cat monolith shut or at the least, cook the washcoat on it.)

If your cars rough running was down to misfire caused by DIS coil failure alone, the engine control would flag misfire on the cylinder, the oxygen sensor would measure out of range HC values & fluctuating air to fuel ratios would confuse the part throttle calibration & try to compensate to meet the smooth running values.

The DIS units are driven direct from withn the DME by low side drivers hard mounted on the mother board in a cluster. The DME will compensate for a percentage of degradation in values that emission related electronic sensors are subject to.
If a new DIS coil is introduced, it should respond pretty quickly but consider that the pre-cat oxygen sensor, spark plug & sooted combustion chamber may not. Some modern plugs do not recover from fuel wetting & have to be replaced & close coupled pre- cat sensors can also be contaminated & need a clean or at worst replaced, but DTC codes or a data logger measuring voltage response valves will confirm this.

I would suggest that if you unplug the ground lead from the battery for approx 35 mins to allow the DME TO reset to factory learn values, you will have your answer
on wether the system is happy or wether a plug may need changing as well.

Quoted:
Steve
Unplugging the ground lead will do nothing except force you to reset your clock & radio stations & is common practise when working on the car.
If you do this & drive the car hard straight afterward ( allow water oil to get to temp) you should experience sharper throttle response & better
part throttle economy.

Quoted:
I had my ECU replaced earlier in the year, it's fine when driving along but seems to misfire on tick over, no management lights on at all and the dealer can find nothing that shows up on their machine

Quoted:
Is car less than 3 yrs ?
Whats the mileage on the car.
Get the emissions measured by a MOT station for HC & CO if when car is at or near static & idle.
If the problem was under load whilst driving & not codes, a rolling road & data logger would
get past the codes issue.
Is problem from cold start or when engine is warm ?

Problem exists with cold or warm engine. Only on tick over or very low revs and never at speed.

Quoted:
Dunnit............hard to tell whether it's any better as it was running far better anyway. I think it helps having 4 pistons consistently firing, rather than only 3 .... Plugs are all brand new following a recent major service.

Thanks for the advice, is that something you'd recommend doing periodically?...............