Moving the impact points of the rounds about deliberatly fell under two other common labels.  Shifting Targets, which could be done at the command of the FO, or by a preplanned schedule/fireplan.  The other was called a Zone & Sweep.   This was a specialized mission designed to evenly saturate a area with projectiles.  In the first case the intial rounds for each target could be fired as a TOT.  In the second case the intial rounds would likely be fired as a TOT, but the subsequent rounds would either be 'When Ready' or on a time line or schedule.

So TOT as we used the term was a seperate item from shifting impact points or targets about.

The TOT thing goes back to ancient times. Cutting loose with all the guns at once makes for a more satifying big bang, can scare the enemy for a few minutes, and is susposed to gain a few more casualties due to suprise.  Think of musketeers firing in volleys, or a line of cannon cutting loose at once on a advancing mass of infantry.  For indirect fires it was used in WWI under other labels as well.

Just to add to Carl's response -

Under usual conditions, the first rounds of artillery to land cause many more casualties than any subsequent rounds (humans having a normally healthy instinct for self-preservation tend to find cover very quickly).

Thus it is in your best interest to have as many rounds as possible land simultaneously, in that first volley, when everyone is still "hanging out".

Yeah, the Americans of course...in WWII (that was wiki I believe no reference, so I dont give that any credit)

The other was a Danish website I believe, suggesting something in the WWI time frame by the British.  It was in a link to a link from a somewhat unrelated subject (history of tank warfare in Western Europe I believe, it was a bit late at night...). 

Anyways, that was the one that got me thinking about TOT again.  As I was trying to find the site again there were a number of websites describing the other tactics as TOT. 

So lets assume the FO of battery A calls for a fire mission on target 1.  The other batterys in that battalion can monitoring the same circut.  If the battalion CO or officer on watch in the CP decides the target rates fires from the entire battalion he gives the following order over the comm  circut: "Battalion;  Target 1; Adjust Fire Battery A;  Battalion  Six Rounds in Effect.   This alerts the other batterys, confirms that battery A is to continue to fire adjusting rounds, that the other batterys are to follow the adjustments on their charts, and the others should have computations for the FFE ready.  When the adjustment is complete the order "Battalion; FFE Target 1; Time on Target 08:32" is given.

To save time standard items like projectile, fuze, ect.. can be established previous and included in the fire order only when a deviation from the standaard is called for.

There is of course the option of skipping the adjusting rounds and call for a FFE directly.  This is commonly done for prelanned targets, or when speed is necessary.  It is fairly common for each battery to follow the adjustments of the others on registration points and preplanned targets.

This all can be reproduced at the next levels.  Each battalion CP passes locations of critical targets to the regiment/brigade and higher which would be passed to the other battalions.  It was also fairly common to have a conduct of fire communications circut for a regiment or a group of brigades, So that when a battery FO spotted a appropriate target several battalions could join the mission.  With these methods it was possible to mass group of 3-4 battalions on a target of opportunity nearly as fast as a single battery.   

It varys by situation.  In the case I refered to the circumstances allowed very tight timing.  The rounds that were five seconds off were quite obvious.  In other situations that much precision would be unobtainable or irrelevant.

With 105mm howitzers the effctive casualty radius is roughly 15 to 25 meters.  The typical probable error for point of impact falls between ten and thirty meters depending on the range & other conditions.  I vaguely recall from the artillery school days the student Lts had to get the adjusting rounds within 25 meters of the target.

Air bursts are generally desired as they have more effcient fragmentation patterns than graze or surface detonating.  Soldiers under cover in ditches & the other micro terrain are not protected from air bursts as they are from surface bursts.  

We usually went for Suppresion or a bit less often Nuetralization results.  Those terma vary in use in different armys & eras.  In our case suppresion could be defined as: Unable to effectively fire or manuver until the attack ceases.  Casualtys are 0 to 2%.  Our concept of nuetralization was: Unable to fire or manuver effectively after the attack ceases long enough to manuver past or to the target.  Casualties would range fro 3% to approaching 15%.  Obviously the volume of fire to 'Nuetralize a company is going to be different from that for a rifle squad or MG team.   And, the time of nuetralization after the attack will vary.   A squad can rush past a 'nuetralized' MG position in a minute or two.  A nuetralized company has to stay that way for a quarter hour or more to get another company into or past its position.

A third term we seldom used was the Destruction mission.  Casualtys necessary for Destruction started at 20% and upwards from 50% might be required for some target types.  Destruction missions required vast quantities of ammunition and we only contemplated them vs very high priority targets, a senior HQ or a nuclear/chemical weapons site.  Even in those cases a artillery nuetralization attack followed by a airstrike or ground assualt was prefered to shooting off many tons of ammo.

Our concepts and techniques of fire were very different from WWI and reflect entirely different tactical and logisitcs conditions.