In other words there is no new sudden mystical collapse process
There will be components of the particle state vector which do not agree with the state vector of the screen. Those components disperse into the wider, noisy environment, much like the splash from a stone thrown into a rough, turbulent ocean. The Schrödinger equation continues to apply to all those components, controlling their evolution in time. In other words, there is no new sudden mystical "collapse" process. However, once those components have dispersed into the "ocean", it becomes effectively impossible to regenerate the original superposition state (this explains why the apparent "collapse of the wavefunction" is an irreversible process). Those superposition elements — to all intents and purposes — disappear. The particle is then detected in only one position: on the screen.
In his book, The Fabric of the Cosmos, Brian Greene describes the process: "Decoherence forces much of the weirdness of quantum physics to leak from large objects since, bit by bit, the quantum weirdness is carried away by the innumerable impinging particles from the environment."
So it is almost impossible to completely isolate an object from the rest of the world. But if we want to maintain a superposition state inside our quantum computer, we need to find some way of achieving that isolation, and thereby preventing that onset of decoherence. Let us now examine how we can achieve that isolation.
