  The dynamical evolution of boson stars in scalar-tensor theories of gravity
is considered in the physical (Jordan) frame. We focus on the study of
spontaneous and induced scalarization, for which we take as initial data
configurations on the well-known S-branch of a single boson star in general
relativity. We show that during the scalarization process a strong emission of
scalar radiation occurs. The new stable configurations (S-branch) of a single
boson star within a particular scalar-tensor theory are also presented.
