There is no single accepted theory about the mechanism of the collapse of quantum wavefunctions. There are many theories that try to explain this. What is known is that a wavefunction is found in a superposition of several eigenstates, and by interaction with the external world the wave collapses into one single eigenstate.
One theory explains that the different eigenstates don't in fact collapse but keep on existing in parallel realities. This is called the "many-worlds interpretation".