We investigate rotating Einstein-Maxwell-Dilaton (EMd) black holes in odd
dimensions. Focusing on black holes with equal-magnitude angular momenta, we
determine the domain of existence of these black holes. Non-extremal black
holes reside with the boundaries determined by the static and the extremal
rotating black holes. The extremal EMd black holes show proportionality of
their horizon area and their angular momenta. Thus the charge does not enter.
We also address the Einstein-Maxwell case, where the extremal rotating black
holes exhibit two branches. On the branch emerging from the Myers-Perry
solutions their angular momenta are proportional to their horizon area, whereas
on the branch emerging from the static solutions their angular momenta are
proportional to their horizon angular momenta. Only subsets of the near-horizon
solutions are realized globally. Investigating the physical properties of these
EMd black holes, we note that one can learn much about the extremal rotating
solutions from the much simpler static solutions. The angular momenta of the
extremal black holes are proportional to the area of the static ones for the
Kaluza-Klein value of the dilaton coupling constant, and remain analogous for
other values. The same is found for the horizon angular velocities of the
extremal black holes, which possess an analogous behavior to the surface
gravity of the static black holes. The gyromagnetic ratio is rather well
approximated by the `static' value, obtained perturbatively for small angular
momenta.Comment: 40 pages, 10 figure
