Integrating distributed sensors in the skin of robot hands is challenging, as the space is limited. This paper presents a dense and small tactile sensor system that can be installed on robotic hands. In the current implementation, the system is constituted by modules that are 26mm long and 27mm wide and they have been successfully integrated on the internal side of each finger phalange of the commercially available Allegro Hand (except the fingertips). Each sensor module contains 16 tri-axial taxels; each taxel is able to measure the applied 3D force vector using a Hall effect sensor and a magnet. The sensor modules are 4mm high, including the printed circuit board (PCB) with the sensors and the soft silicone with the magnets. The back of the PCB is flat without any components mounted, which eases the integration. Each sensor has I2C digital output, and each sensor module is connected to four I2C buses, requiring only seven wires for each module. The tri-axial taxels are close to each other (4.7 mm from the center of one taxel to the next), but experiments proved that independent force vectors can be measured and that the crosstalk is limited.