Through their normal operation, cellular networks are a repository of continuous location information from their subscribed devices. Such information, however, comes at a coarse granularity both in terms of space, as well as time. For otherwise inactive devices, location information can be obtained at the granularity of the associated cellular sector, and at infrequent points in time, that are sensitive to the structure of the network itself, and the level of mobility of the device. In this paper, we are asking the question of whether such sparse information can help to identify the paths followed by mobile connected devices throughout the day. If such a task is possible, then we would not only enable continuous mobility path estimation for smartphones, but also for the millions of future connected "things". The challenge we face is that cellular data has one to two orders of magnitude less spatial and temporal resolution than typical GPS traces. Our contribution is to devise path segmentation, de-noising, and inference procedures to estimate the device stationary location, as well as its mobility path between stationary positions. We call our technique Cell∗. We complement the lack of spatio-temporal granularity with information on the cellular network topology, and GIS (Geographic Information System). We collect more than 3,000 mobility trajectories over 8 months and show that Cell∗achieves a median error of 230m for the stationary location estimation, while mobility paths are estimated with a median accuracy of 70m. We show that mobility path accuracy improves with its length and speed, and counter to our intuition, accuracy appears to improve in suburban areas. Cell∗is the first technology, we are aware of, that allows location services for the new generation of connected mobile devices, that may feature no GPS, due to cost, size, or battery constraints.