We present 2.5-D global, ideal MHD simulations of magnetically and rotationally driven protostellar jets from Keplerian accretion discs, wherein only the initial magnetic field strength at the inner radius of the disc, $B_{rm i}$, is varied. Using the AMR-MHD code AZEUS, we self-consistently follow the jet evolution into the observational regime ($>10^3,mathrm{AU}$) with a spatial dynamic range of $sim6.5times10^5$. The simulations reveal a three-component outflow: 1) A hot, dense, super-fast and highly magnetised jet core; 2) a cold, rarefied, trans-fast and highly magnetised sheath surrounding the jet core and extending to a tangential discontinuity; and 3) a warm, dense, trans-slow and weakly magnetised shocked ambient medium entrained by the advancing bow shock. The simulations reveal power-law relationships between $B_{rm i}$ and the jet advance speed, $v_{rm jet}$, the average jet rotation speed, $langle v_varphirangle$, as well as fluxes of mass, momentum, and kinetic energy. Quantities that do not depend on $B_{rm i}$ include the plasma-$beta$ of the transported material which, in all cases, seems to asymptote to order unity. Jets are launched by a combination of the magnetic tower and bead-on-a-wire mechanisms, with the former accounting for most of the jet acceleration---even for strong fields---and continuing well beyond the fast magnetosonic point. At no time does the leading bow shock leave the domain and, as such, these simulations generate large-scale jets that reproduce many of the observed properties of protostellar jets including their characteristic speeds and transported fluxes.
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