  We investigate the stationary and dynamical behavior of an Anderson localized
chain coupled to a single central bound state. The coupling to the central site
partially dilutes the Anderson localized peak towards the nearly resonant
sites. In particular, the number of resonantly coupled sites remains finite in
the thermodynamic limit. This is further supported by a multifractal analysis
of eigenstates that shows the frozen spectrum of fractal dimension, which is
characteristic for localized phases in models with power-law hopping. Although
the well-known Fano-resonance problem is seemingly similar to our system, it
fails to describe it because of the absence of level repulsion within the
energy spectrum. For weak coupling strengths to the central site, we identify a
regime with a logarithmic in time transport of particles and information.
