  We analyze the entanglement properties of spins (qubits) close to the
boundary of spin chains in the vicinity of a quantum critical point and show
that the concurrence at the boundary is significantly different from the one of
bulk spins. We also discuss the von Neumann entropy of dissipative environments
in the vicinity of a (boundary) critical point, such as two Ising-coupled
Kondo-impurities or the dissipative two-level system. Our results indicate that
the entanglement (concurrence and/or von Neumann entropy) changes abruptly at
the point where coherent quantum oscillations cease to exist. The phase
transition modifies significantly less the entanglement if no symmetry breaking
field is applied and we argue that this might be a general property of the
entanglement of dissipative systems. We finally analyze the entanglement of an
harmonic chain between the two ends as function of the system size.
