Solution adaptive grid strategies based on the redistribution of a fixed number of points are described in this paper. The redistribution is performed using weight functions that vary based on significant flow features. The weight functions are evaluated using an equidistribution principle. In this paper, emphasis is placed on the development of weight functions applicable to compressible flows exhibiting large scale separated vortical flows, vortex-vortex and vortex-surface interactions, separated shear layers and multiple shocks of different intensities. Algebraic, elliptic and parabolic methods of grid generation have been utilized for structured grid redistribution. Additionally, a point movement scheme is presented for generalized (structured/unstructured/hybrid) grid adaptation. Computer Aided Geometry Design (CAGD) techniques are combined with redistribution schemes to maintain the fidelity of solid boundaries. In particular, solid boundaries are represented using Non-Uniform Rational B-Splines (NURBS). A grid generation software system - Parallel Multiblock Adaptive Grid generation (PMAG) - using an elliptic redistribution scheme is also described with emphasis placed on the parallel implementation for multiblock structured grids with unstructured blocking topologies and on interpolation issues. Computational examples demonstrating the influence of different weight functions and grid redistribution strategies are presented. (C) 2000 Elsevier Science S.A. All rights reserved.