The linear Schrödinger equation does not predict the uniqueness of measurement results; it does not predict that macroscopic bodies should be located at one place in space only. This is the origin of the so called measurement problem, Schrödinger cat paradox, etc. Theories such as GRW (Ghirardi-Rimini-Weber) and CSL (Continuous spontaneous localization) theories solve the problem by adding stochastic terms to the Schrödinger equation. In this talk we will propose another approach to reach the same unified dynamics, but without requiring the introduction of stochastic Wiener processes acting in all space. The method combines ideas of the dBB (de Broglie Bohm) interpretation and of CSL. It introduces an attraction between the space density of Bohmian position and the space density operators, with a deterministic dynamics; randomness arises only from the initial random positions of the Bohmian positions. Various microscopic or macroscopic consequences of this dynamics will be discussed.