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The electronic structure of the ground and some excited states of neutralatoms with the nuclear charge numbers $1\leq Z \leq 10$ and their singlepositive ions are investigated by means of our 2D mesh Hartree-Fock method forstrong magnetic fields $0.5\leq \gamma \leq 10000$. For $\gamma=10000$ theground state configurations of all the atoms and ions considered are given byfully spin-polarized configurations of single-electron orbitals with magneticquantum numbers ranging from m=0 to m=-N+1 where N is the number of theelectrons. Focusing on the fully spin polarized situation we provide criticalvalues of the magnetic field strength for which crossovers with respect to thespatial symmetries of the ground state take place. It is found that the neutralatoms and singly charged positive ions with $2\leq Z \leq 5$ have one fullyspin-polarized ground state configuration whereas for $6\leq Z \leq 10$ oneintermediate fully spin-polarized configuration with an orbital of 2p_0 typeoccurs.Comment: to appear in Physical Review

Ground states of H, He,…, Ne, and their singly positive ions in strong magnetic fields: The high-field regime