  We present a protocol that sets maximum stationary entanglement between
remote spins through scattering of mobile mediators without initialization,
post-selection or feedback of the mediators' state. No time-resolved tuning is
needed and, counterintuitively, the protocol generates two-qubit singlet states
even when classical mediators are used. The mechanism responsible for such
effect is resilient against non-optimal coupling strengths and dephasing
affecting the spins. The scheme uses itinerant particles and scattering centres
and can be implemented in various settings. When quantum dots and photons are
used a striking result is found: injection of classical mediators, rather than
quantum ones, improves the scheme efficiency.
