Fuel cut, T-VSV, actuator and boost are all interconnected.
The actuator is directly connected to the output of the turbo compressor by a dedicated pipe that fits on to a connector on the turbo compressor housing. The actuator has a spring that resists the boost pressure. When the boost pressure exceeds the spring strength the actuator piston/diaphragm moves because of the boost pressure acting upon it. This moves a push road that acts on a lever to open the wastegate that allows the exhaust gasses to bypass the turbine wheel. The turbo slows down, the boost drops and the actuator will close again.
The actuator has another pipe going from it and this goes to the T-VSV. The T-VSV is nothing more (IMHO) than an electronically controlled bleed valve. On the Rev1/2 cars this is either on or off. Normally it is off. When it's off there is no pressure bled away from inside the actuator, so the actuator opens/closed depending on how strong the spring inside there is - and this is the base low boost you get when it's cold or the ECU isn't happy. On the Rev 3 the T-VSV is pulsed by the ECU and this method is used to control how much air bleeds off from the actuator.
The T-VSV....is an electrically operated bleed valve. This bit is for the Rev 1, possibly Rev 2, dunno about the Rev3. The two feeds to the T-VSV are +12Volt and earth. +12volt is applied only when there is no (or little) vacuum in the induction manifold. The T-VSV still won't open though because the earth is floating (it's effectively not connected to anything). When the ECU is happy that all is well it will take the earth wire of the T-VSV and earth it to ground - the current flows and the T-VSV opens. The T-VSV has two switched signals. The +12volts is switched. The earth is switched.
The T-VSV (Rev1 and poss Rev 2) bleeds air away from the actuator, the pressure in there drops and so more pressure is required from the boost of the turbo to feed this leak and also push the spring open to operate the actuator and open the wastegate. This extra boost is the 3psi or so that people see - this takes the stock 7psi (roughly) up to 10psi (roughly) that we know and love on Rev1/2 tubbies.
Fuel cut. I mentioned the induction manifold pressure has to be either no or little vacuum. This bit is Rev1/2 only. There is a pressure sensor that is plumbed into the induction manifold and measures pressure between the throttle butterfly valve and the cylinders. This sensor output is measured by the ECU - if the voltage goes too high - and so the boost goes too high the ECU switches into fuel cut mode which lasts until the ignition is turned off (room for discussion on this, but on my Rev 1 you need to turn the ignition off).
If the boost goes too high the ECU will fuel cut (and put the ECU warning lamp on for a few seconds) - and it is very very harsh - there's no doubting when it happens. Until the ignition is turned off the ECU will fuel cut whenever it sees any boost - in fact, it's the same threshold used to decide when to apply +12volts to the T-VSV. When in this mode you will have fuel cut whenever any positive boost is generated. Turn the ignition off and then on again and the ECU leaves this mode and runs normally - until it overboosts again.
The T-VSV is a fine idea, but as you can see a common way to disable the T-VSV is either to block the hose going from the actuator to the T-VSV (the bleed valve is open, but there's no air getting past the blockage - so it doesn't bleed air off) or break the electrical circuit that feeds the T-VSV.
Many people have modified the connection to the T-VSV that the ECU uses such that a switch earths the T-VSV rather than the ECU. Others put a three way switch in there so the T-VSV can either be turned off, controlled by the ECU or always on..
It's all well and good until you come to fit some other sort of boost controller. The T-VSV typically adds 3 or 4psi to the stock boost. Increasing the boost can be done a number of ways, either by putting in an actuator with a stronger spring, or by bleeding air off in some way. If a different actuator is used the T-VSV will still bleed air out if activated and will bleed air out to give a higher boost increase than 3 or 4psi because there's more air escaping because the pressure difference between inside the actuator and atmosphere is higher. This is ok I suppose, but not desirable.
Most people increase boost pressure by putting in a second bleed valve (counting the T-VSV as the first bleed valve) or a Grainger valve. Each method has it's little differences but in general a G-valve only passes air to the actuator once the boost pressure reaches a high enough point to overcome the resistance of a spring inside the G valve. The spring opens, the seal is broken and the boost pressure suddenly acts on the actuator - and it snaps open. The turbo slows down, the boost drops and the spring in the G valve closes. I've no idea how the pressure between the G valve and the actuator escapes, never have understood that and probably never will. The G valve causes the actuator to snap open and closed, so boost builds more quickly.
A bleed valve works like the T-VSV except it's always open and air is always bled out under boost, however the boost pressure does act upon the actuator all the time so with bleed valve cars the actuator can tend to open as the desired and preset boost level is approached causing boost to build to the predefined level more slowly.
The boost pressure is predefined in a G valve by adjusting the strength of the spring inside the valve - usually achieved by turning a locking threaded nut/bolt thing within the G valve which either squishes the spring inside more (so it takes more force to open it), or loosens the spring inside (so it takes less pressure to open it). A bleed valve the hole that allows the boost pressure to trickle out is either made bigger or smaller.
Electronic boost controllers have a solenoid valve in them that allows the boost pressure to pass to the actuator, or allows the boost pressure to be blocked and opens the actuator to atmosphere. This transfer valve (the actuator is connected to the boost pressure line, or it's connection is transferred to atmosphere) is controlled by a solenoid and that is switched or pulsed by the electronic gubbins.
Right, the reason that people disable T-VSVs (myself included) is that when running elevated boost the ECU doesn't know what it's playing at and IMHO can mess things up. I run an AVC-R and with the T-VSV connected the boost pressure spikes like a good'un to dangerously high levels. With the T-VSV installed and live it can tend to cause problems with other boost controllers, either G valves, bleed valves or electronic boost controllers.
Again, IMHO if you're going to be adjusting boost you'll need an accurate boost gauge of some kind. I'm spoilt by having the AVC-R as it records boost pressures, but even there I still have an Omori boost gauge - and that's the one I use.
So, that relationship...
Boost is generated. The actuator and T-VSV combine such that at 7 or 8psi (T-VSV is closed - ie. it's cold or the ECU has thrown it's toys out) of boost is generated the actuator will start to open. Exhaust gasses bypass the turbine, the turbo slows down and boost drops - the actuator spring overcomes the boost pressure and pushes the actuator closed - a few cycles and it balances to 7 or 8 psi. If the ECU is happy the T-VSV will open when it sees +ve boost and bleed sufficient air off to give a 3 or 4psi increase in boost before the actuator spring force is overcome by the boost pressure and the actuator opens - same as before, the actuator opens the wastegate, the exhaust gasses bypass the turbine and the turbo slows down, boost drops and the spring in the actuator pushes the actuator closed, closing the wastegate and allowing the exhaust to drive the turbine again.
Boost is always being measured by the boost pressure sensor (Rev 1/2). If the ECU decides the boost pressure rises over some preset amount it goes into fuel cut mode where it stops the injectors from firing until the +ve boost goes away. If +ve boost is detected again it stops the injectors - until the ECU is reset by turning the ignition off and on (on my Rev 1 at least).