Depleted Monolithic Active Pixel Sensor (DMAPS) sensors developed in the Tower Semiconductor 180 nm CMOS imaging process have been designed in the context of the ATLAS ITk upgrade Phase-II at the HL-LHC and for future collider experiments. The "MALTA-Czochralski (MALTA-Cz)" full size DMAPS sensor has been developed with the goal to demonstrate a radiation hard, thin CMOS sensor with high granularity, high hit-rate capability, fast response time and superior radiation tolerance. The design targets radiation hardness of > 10(15) (1 MeV) n(eq)/cm(2) and 100 Mrad TID. The sensor shall operate as tracking sensor with a spatial resolution of approximate to 10 mu m and be able to cope with hit rates in excess of 100 MHz/cm(2) at the LHC bunch crossing frequency of 40 MHz. The 512 x 512 pixel sensor uses small collection electrodes (3.5 mu m) to minimize capacitance. The small pixel size (36.4 x 36.4 mu m(2)) provides high spatial resolution. Its asynchronous readout architecture is designed for high hit-rates and fast time response in triggered and trigger-less detector applications. The readout architecture is designed to stream all hit data to the multi-channel output which allows an off-sensor trigger formation and the use of hit-time information for event tagging.The sensor manufacturing has been optimised through process adaptation and special implant designs to allow the manufacturing of small electrode DMAPS on thick high-resistivity p-type Czochralski substrate. The special processing ensures excellent charge collection and charge particle detection efficiency even after a high level of radiation. Furthermore the special implant design and use of a Czochralski substrate improves the sensor's time resolution. This paper presents a summary of sensor design optimisation through process and implant choices and TCAD simulation to model the signal response. Beam and laboratory test results on unirradiated and irradiated sensors have shown excellent detection efficiency after a dose of 2 x 10(15) 1 MeV n(eq)/cm(2). The time resolution of the sensor is measured to be sigma = 2 ns.