  We study theoretically the effects of disorder on Bose-Einstein condensates
(BEC) of bosonic triplon quasiparticles in doped dimerized quantum magnets. The
condensation occurs in a strong enough magnetic field Hc, where the
concentration of bosons in the random potential is sufficient to form the
condensate. The effect of doping is partly modeled by delta - correlated
disorder potential, which (i) leads to the uniform renormalization of the
system parameters and (ii) produces disorder in the system with renormalized
parameters. These approaches can explain qualitatively the available
magnetization data in the Tl_(1-x)K_(x)CuCl_3 compound taken as an example. In
addition to the magnetization, we found that the speed of the Bogoliubov mode
has a peak as a function of doping parameter, x. No evidence of the pure Bose
glass phase has been obtained in the BEC regime.
