  We investigate the real-time dynamics of open quantum spin-$1/2$ or hardcore
boson systems on a spatial lattice, which are governed by a Markovian quantum
master equation. We derive general conditions under which the hierarchy of
correlation functions closes such that their time evolution can be computed
semi-analytically. Expanding our previous work [Phys. Rev. A 93, 021602 (2016)]
we demonstrate the universality of a purely dissipative quantum Markov process
that drives the system of spin-$1/2$ particles into a totally symmetric
superposition state, corresponding to a Bose-Einstein condensate of hardcore
bosons. In particular, we show that the finite-size scaling behavior of the
dissipative gap is independent of the chosen boundary conditions and the
underlying lattice structure. In addition, we consider the effect of a uniform
magnetic field as well as a coupling to a thermal bath to investigate the
susceptibility of the engineered dissipative process to unitary and nonunitary
perturbations. We establish the nonequilibrium steady-state phase diagram as a
function of temperature and dissipative coupling strength. For a small number
of particles $N$, we identify a parameter region in which the engineered
symmetrizing dissipative process performs robustly, while in the thermodynamic
limit $N\rightarrow \infty$, the coupling to the thermal bath destroys any
long-range order.
