  Merging double compact objects (CO) represent the inferred sources of every
detected gravitational wave (GW) signal, thus modeling their progenitors is
important to constrain stellar evolution theory. Stable mass transfer (MT)
between a donor star and a black hole is one of the proposed tightening
mechanisms to form binary black holes merging within the age of the universe.
We aim to assess the potential of stable non conservative mass transfer to
produce the pairings of COs: black holes (BHs), neutron stars (NSs) and white
dwarfs (WDs). We study the conditions required for mass transfer between a star
and a CO to be stable and to lead to merging binary COs. We use published
results for the response of the stellar radii to rapid mass loss; coupled with
analytical models for orbital evolution, we determine the boundary for unstable
MT and the post interaction properties of binaries undergoing stable MT. We
investigate the impact of angular momentum loss prescription in the hardening
by accounting for isotropic re emission from the accretor vicinity and mass
outflow from the Lagrangian point L2. Stable MT in systems with a CO + Roche
lobe filling star, in the limit of isotropic re-emission, is shown to be able
to form any pair of merging COs apart from WD + BH. Considering mass outflow
from L2, the resulting parameter space for GW progenitors is shifted towards
smaller initial mass ratios, ruling out the formation of NS + NS while allowing
the production of merging WD + BH pairs. We compare our results with
single-degenerate binaries and find that conditions for stable MT to operate
are present in nature. We show that stable MT in the isotropic re-emission
limit can produce merging binary BHs with mass ratios consistent with the
majority of inferred sources of the third Gravitational Wave Transient
Catalogue. Angular momentum loss from L2 lifts the achievable final mass ratio.
