Abstract: More than 20 years ago at the beginning of the RHIC era, a new nucleus-nucleus initial state was proposed, based on the longitudinal Effective String Rope Model for further 3+1D relativistic fluid dynamical evolution. The big advantage of this initial state, in comparison to others available at that time, was that it reflected correctly not only the energy-momentum, but also angular momentum conservation laws. Consequently, such an initial state for non-central ultra-relativistic heavy ion collisions may lead to overall rotation of the reaction volume or/and to a large vorticity of the collective flow, which can manifest itself via polarization of emitted particles. This is supported by the observations of global polarization of Lambda and anti-Lambda hyperons at non-zero impact parameter in Au+Au collisions at RHIC reported by STAR collaboration.

In the last two decades with the construction of high energy colliders, such as the Large Hadron Collider at CERN, as well as with the development of new detectors and new data storing and analyzing methods, the study of heavy ion collisions event-by-event has become possible. In order to perform an analysis of the simulated collisions in a

modern "event-by-event" mode such an initial state model has to be modified.

I will present the Generalized Effective String Rope Model in which the fluctuations in the initial state are taken into account following the Glauber Monte Carlo approach. I will analyze how such fluctuations lead to principal differences in the initial state not only for a single (random) event, but also if we perform an averaging over many events. I will also compare the results obtained in this model for symmetric Au+Au collisions at different impact parameters with those for asymmetric A+Au head on collisions.