  We present a comprehensive study of maximally entangled symmetric states of
arbitrary numbers of qubits in the sense of the maximal mixedness of the
one-qubit reduced density operator. A general criterion is provided to easily
identify whether given symmetric states are maximally entangled in that respect
or not. We show that these maximally entangled symmetric (MES) states are the
only symmetric states for which the expectation value of the associated
collective spin of the system vanishes, as well as in corollary the dipole
moment of the Husimi function. We establish the link between this kind of
maximal entanglement, the anticoherence properties of spin states, and the
degree of polarization of light fields. We analyze the relationship between the
MES states and the classes of states equivalent through stochastic local
operations with classical communication (SLOCC). We provide a nonexistence
criterion of MES states within SLOCC classes of qubit states and show in
particular that the symmetric Dicke state SLOCC classes never contain such MES
states, with the only exception of the balanced Dicke state class for even
numbers of qubits. The 4-qubit system is analyzed exhaustively and all MES
states of this system are identified and characterized. Finally the
entanglement content of MES states is analyzed with respect to the geometric
and barycentric measures of entanglement, as well as to the generalized
N-tangle. We show that the geometric entanglement of MES states is ensured to
be larger than or equal to 1/2, but also that MES states are not in general the
symmetric states that maximize the investigated entanglement measures.
