A laboratory automation system comprising a storage for preservation of biological product containers and a multiple rack apparatus for accommodating biological product containers unloaded from the storage, wherein said multiple rack apparatus comprises an odd number of racks which can be housed within a base platform having a number of locations which is equal to said odd number plus one, said racks being horizontally or vertically slidable from one location to another of said base platform, taking advantage of the presence of a temporarily empty location, said racks, furthermore, in turn occupying an operating location which, being vertical with respect to an outlet tube of said storage, accommodates said biological product containers unloaded from said storage;
- wherein said storage comprises a storage control unit which keeps count of the biological product containers unloaded through said outlet tube into one of said racks which in turn occupies the operating location,
- wherein said multiple rack apparatus comprises a presence sensor adapted to detect the presence of one of said racks in said operating location, said presence sensor being operatively connected to said storage control unit to block said outlet tube until the presence of one of said racks is not detected in said operating location and, when said rack is detected, to automatically resume an unloading operation of said biological product containers through said outlet tube, and
- wherein said storage control unit activates the sliding of said racks from one location to another, when one of said racks which in turn occupies the operating location is fulfilled with a predetermined number of biological product containers.