  In magnets with strong quantum fluctuations, paramagnetic ground states with
or without confinement of spinon excitations can be realized. Here we discuss
the physics of the confined phase in the vicinity of a
confinement--deconfinement transition: This regime, likely relevant to a
multitude of frustrated spin systems, is characterized by multiple length
scales: In addition to the magnetic correlation length, a confinement length
can be defined, which can be probed, e.g., by local static measurements near
non-magnetic impurities. We illustrate the ideas by explicit calculations for
dimerized spin chains, but our qualitative results remain valid in higher
dimensions as well. In particular, we study crossover from weak to strong
confinement visible in the antiferromagnetic polarization cloud around a
non-magnetic impurity. We also discuss the effective magnetic interaction
between impurities, relevant for impurity-induced magnetic order, and
consequences for nuclear magnetic resonance and neutron scattering experiments.
