  Searches for {\it dark matter} sector field imprints on the astrophysical
phenomena are one of the most active branches of the current researches. Using
numerical methods we elaborate the influence of {\it dark matter} on the
emergence of black hole hair and formation of boson stars. We explore
thermodynamics of different states of the system in Einstein-Maxwell-scalar
{\it dark matter} theory with box boundary conditions. Finally we find that the
presence of dark sector within the system diminishes a chance of formation of
scalar hair around a black hole.
