  We aim to hunt for massive binaries hosting a black hole companion (OB+BH)
and establish the natal mass-ratio distribution of massive stars at the
subsolar metallicity environment of the Large Magellanic Cloud (LMC). We use
the shift-and-add grid disentangling technique to characterize the hidden
companions in 51 SB1 O-type and evolved B-type binaries in the LMC monitored in
the framework of the Tarantula Massive Binary Monitoring (TMBM).
  Out of the 51 SB1 systems, 43 (84%) are found to have non-degenerate stellar
companions, of which 28 are confident detections, and 15 are less certain (SB1:
or SB2:). Of these 43 targets, one is found to be a triple (VFTS 64), and two
are found to be quadruples (VFTS 120, 702). The remaining eight targets (16%)
retain an SB1 classification. Aside from the unambiguous case of VFTS 243,
analysed in detailed in a separate paper, we identify two additional OB+BH
candidates: VFTS 514 and VFTS 779. Additional black holes may be present in the
sample but at a lower probability. Our study firmly establishes a virtually
flat natal mass-ratio distribution for O-type stars at LMC metallicity,
covering the entire mass-ratio range (0.05 < q < 1) and periods in the range 0
< log P < 3 [d]. The nature of the OB+BH candidates should be verified through
future monitoring, but the frequency of OB+BH candidates is generally in line
with recent predictions at LMC metallicity.
