  The electronic structure of the ground and some excited states of neutral
atoms with the nuclear charge numbers $1\leq Z \leq 10$ and their single
positive ions are investigated by means of our 2D mesh Hartree-Fock method for
strong magnetic fields $0.5\leq \gamma \leq 10000$. For $\gamma=10000$ the
ground state configurations of all the atoms and ions considered are given by
fully spin-polarized configurations of single-electron orbitals with magnetic
quantum numbers ranging from m=0 to m=-N+1 where N is the number of the
electrons. Focusing on the fully spin polarized situation we provide critical
values of the magnetic field strength for which crossovers with respect to the
spatial symmetries of the ground state take place. It is found that the neutral
atoms and singly charged positive ions with $2\leq Z \leq 5$ have one fully
spin-polarized ground state configuration whereas for $6\leq Z \leq 10$ one
intermediate fully spin-polarized configuration with an orbital of 2p_0 type
occurs.
