Terahertz (THz) integrated sensing and communication (ISAC) enables simultaneous data transmission with Terabit-per-second (Tbps) rate and millimeter-level accurate sensing. To realize such a blueprint, ultra-massive antenna arrays with directional beamforming are used to compensate for severe path loss in the THz band. In this paper, the time-frequency-space transmit design is investigated for THz ISAC to generate time-varying scanning sensing beams and stable communication beams. Specifically, with the dynamic array-of-subarray (DAoSA) hybrid beamforming architecture and multi-carrier modulation, two ISAC hybrid precoding algorithms are proposed, namely, a vectorization (VEC) based algorithm that outperforms existing ISAC hybrid precoding methods and a low-complexity sensing codebook assisted (SCA) approach. Meanwhile, coupled with the transmit design, parameter estimation algorithms are proposed to realize high-accuracy sensing, including a wideband DAoSA MUSIC method for angle estimation and a sum-DFT-GSS approach for range and velocity estimation. Numerical results indicate that the proposed algorithms can realize centi-degree-level angle estimation accuracy and millimeter-level range estimation accuracy, which are one or two orders of magnitudes better than the methods in the millimeter-wave band. In addition, to overcome the cyclic prefix limitation and Doppler effects, an inter-symbol interference- and inter-carrier interference-tackled sensing algorithm is developed to refine sensing capabilities for THz ISAC.