Quasi-static magnetic-fields up to $800\,$T are generated in the interaction of intense laser pulses ($500\,$J, $1\,$ns, $10^{17}\,$W/cm$^2$) with capacitor-coil targets of different materials. The reproducible magnetic-field peak and rise-time, consistent with the laser pulse duration, were accurately inferred from measurements with GHz-bandwidth inductor pickup coils (B-dot probes). Results from Faraday rotation of polarized optical laser light and deflectometry of energetic proton beams are consistent with the B-dot probe measurements at the early stages of the target charging, up to $t≈ 0.35\,$ns, and then are disturbed by radiation and plasma effects. The field has a dipole-like distribution over a characteristic volume of $1\,$mm$^3$, which is coherent with theoretical expectations. These results demonstrate a very efficient conversion of the laser energy into magnetic fields, thus establishing a robust laser-driven platform for reproducible, well characterized, generation of quasi-static magnetic fields at the kT-level, as well as for magnetization and accurate probing of high-energy-density samples driven by secondary powerful laser or particle beams. ; Comment: 16 pages, 7 figures