  The axion field, the angular direction of the complex scalar field associated
with the spontaneous symmetry breaking of the Peccei-Quinn (PQ) symmetry, could
have originated with initial non-zero velocity. The presence of a non-zero
angular velocity resulting from additional terms in the potential that
explicitly break the PQ symmetry has important phenomenological consequences
such as a modification of the axion mass with respect to the conventional PQ
framework or an explanation for the observed matter-antimatter asymmetry. We
elaborate further on the consequences of the "kinetic misalignment" mechanism,
assuming that axions form the entirety of the dark matter abundance. The
kinetic misalignment mechanism possesses a {\it weak} limit in which the axion
field starts to oscillate at the same temperature as in the conventional PQ
framework, and a {\it strong} limit corresponding to large initial velocities
which effectively delay the onset of oscillations. Following a UV-agnostic
approach, we show how this scenario impacts the formation of axion
miniclusters, and we sketch the details of these substructures along with
potential detecting signatures.
