An original approach to flux growth has been developed to provide for the first time large and high-quality single crystals of oxygen deficient LnBaCO(2+delta) (Ln = Eu, Gd, Tb, Dy, Tb0.9Dy0.1). The data from DTA studies of both the BaO-CoO binary eutectic and temperature of crystal nucleation as well as analysis of more than 100 runs of sub-liquidus co-crystallization allow one to infer the tentative (T-x) phase diagram of a quasi-binary cut in the Ln(2)O(3)-BaO-CoO system with the estimated primary crystallization field for the LnBaCo(2)O(5+delta) (Ln-112) phase. As a result, in successful growth runs several crystals of a parallelepiped shape and up to 120mm(3) in volume were grown. The dependence of the crystal shape on the rare earth ion is discussed. For most flux melts close to the ternary eutectic compositions of the corresponding quasi-binary cuts, co-crystallization of the layered cobaltite phase and a new one of LnBaCo(4)O(7) (Ln-114) was found in a wide range of temperatures. Data on the twinned crystal structure of the optimally oxidized (delta = 0.5) orthorhombic Ln-112 crystals and crystal characterization by chemical composition, magnetic susceptibility and resonance photoemission spectroscopy are discussed. (c) 2004 Elsevier B.V. All rights reserved.