After having outlined the uses of new technologies such as smartphones, touch-screen tablets, and laptops, this article presents the TangiSense interactive tabletop, equipped with RFID technology tagged on tangible objects, as a new paradigm of interaction for ambient intelligence. Within its framework, this article aims to distribute surfaces (tables) interacting mainly with tangible objects. Leads for interactive surface distribution such as interactive tables are given. The article proposes to describe some tangible objects, which are the interaction supports; these are called Tangigets. They are defined according to an augmented Presentation-Abstraction-Control structure to take the tangibility element into account. Six categories of Tangigets are also proposed, which are tangible objects, and the supports of distributed collaboration. To validate the Tangiget concept and its use on the TangiSense tabletop, illustrations in centralized and distributed configurations are proposed. A first evaluation is also presented. To conclude, the article presents the directions under consideration for our future research.