Parking is a major problem of car transportation, with important implications in traffic congestion and urban landscape. Reducing the space needed to park cars has led to the development of fully automated and mechanical parking systems. These systems are, however, limitedly deployed because of their construction and maintenance costs. Leveraging on semi and fully-autonomous vehicular technology, as well as on the electric propulsion paradigm and in vehicular ad hoc networking, we propose a new parking concept where the mobility of parked vehicles is managed by a parking lot controller to create space for cars entering or exiting the parking lot, in a collaborative manner. We show that the space needed to park such vehicles can be reduced to half the space needed with conventional parking lot designs. We also show that the total travelled distance of vehicles in this new parking lot paradigm can be 30% less than in conventional parking lots. Our proposal can have important consequences in parking costs and in urban landscape.