  In this paper we consider singular timelike spherical hypersurfaces embedded
in a $D$-dimensional spherically symmetric bulk spacetime which is an
electrovacuum solution of Einstein equations with cosmological constant. We
analyse the different possibilities regarding the orientation of the gradient
of the standard $r$ coordinate in relation to the shell. Then we study the
dynamics according to Einstein equations for arbitrary matter satisfying the
dominant energy condition. In particular, we thoroughly analyse the asymptotic
dynamics for both the small and large-shell-radius limits. We also study the
main qualitative aspects of the dynamics of shells made of linear barotropic
fluids that satisfy the dominant energy condition. Finally, we prove weak
cosmic censorship for this class of solutions.
