 The key assumption of QMSL is the following: each elementary constituent of any physical system is subjected, at random times, to random and spontaneous localization processes (which we will call hittings) around appropriate positions. To have a precise mathematical model one has to be very specific about the above assumptions, making explicit HOW the process works (which modifications of the wave function are induced by the localizations), WHERE it occurs (what determines the occurrence of a localization at a certain position rather than at another one), and finally WHEN (at what times), it occurs. The answers to these questions are now presented.