Coarse-grained molecular simulations of a model of a T-shaped polyphilic molecule in the presence of solvents are presented. The target molecules are liquid crystal bolaamphiphiles with grafted lateral side chains. The main core of the molecule corresponds to a rigid biphenyl unit, decorated at both ends with polar associating sites. A lateral flexible chain, whose character is mostly antagonistic with respect to the rest of the molecule, imparts unique self-assembly behavior to the pure fluid. In the case herein, the pure T-shaped bolaamphiphile (TsB) forms two-dimensional honeycomb-like columnar structures, and a study is performed on the effects of solvents added to this structure. Three model solvents are considered, each corresponding to the three different parts of the original molecule. We consider the whole concentration range and a temperature at which the pure TsB fluid shows a columnar liquid crystal behavior. All three solvents show different progressions and equilibrium mesophases. The solvent compatible with the end groups swells the structure at low concentrations and at higher concentrations forces a phase split between an essentially pure solvent phase and a structured LC phase. The solvent affine with the core of the TsB does not swell the structure at low concentrations. At higher concentrations, this solvent induces a phase separation where the TsB-rich phase forms a unique liquid crystal membrane. The solvent compatible with the lateral chain will not form stable phase separations, but transforms the columnar structure into a loose, worm-like micellar network. The results reported are generic in nature and describe the phase space for the entire family of TsB's.