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 $tapprox 0.35,$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.