Assembling system between columns and a slab and construction process therefore

A concrete slab assembling system comprising: -a reinforced concrete slab (1); -a supporting column (2); -a supported column (3), having a bottom-end with a reference outer diameter thereof; -an interface adaptor (10) for placement between the supported column bottom-end and the slab top surface; -said interface adaptor (10) outer diameter at least at the contacting portion with said bottom-end surface, being at least 10% smaller than the reference diameter of the supported column. The invention also provides the corresponding method for assembling a concrete slab (1) between a supporting column (2) and a supported column (3).