  We outline transient quasi-magnetostatic phenomena associated with
Weibel-type instabilities, mainly, the formation and decay of the current
sheets and filaments. We consider a collisionless anisotropic plasma cloud with
hot electrons expanding into an inhomogeneous background plasma taking into
account an external magnetic field in different geometries entailing (i) a
hot-electron spot of a circular or cylindrical form within an initial-value
problem or a finite-time injection of electrons from a target surface, (ii)
inhomogeneous layers of cold background plasma of different densities and
spatial scales, (iii) an external magnetic field with three orientations:
perpendicular to the target or along it, directed either across or parallel to
a long axis of the hot-electron spot. We heed typical laser-plasma experiments.
We outline development of the principle current structures linked with distinct
forms of the anisotropic electron velocity distribution using particle-in-cell
modeling of the instability process for diverse sets of the attributes
(i)--(iii). Applications to the analysis of laboratory and space plasma
problems involving an explosive development of the small-scale filamentation of
the electric current and self-consistent magnetic turbulence are discussed.
