  We construct a new class of Einstein-Maxwell static solutions with a magnetic
field in $D$-dimensions (with $D\geq 5$ an odd number), approaching at infinity
a globally Anti-de Sitter (AdS) spacetime. In addition to the mass, the new
solutions possess an extra-parameter associated with a non-zero magnitude of
the magnetic potential at infinity. Some of the black holes possess a
non-trivial zero-horizon size limit, which corresponds to a solitonic
deformation of the AdS background.
