  Quantum phase transitions (QPTs) have been studied extensively in correlated
electron systems. Characterization of magnetism at QPTs has, however, been
limited by the volume-integrated feature of neutron and magnetization
measurements and by pressure uncertainties in NMR studies using powderized
specimens. Overcoming these limitations, we performed muon spin relaxation
($\mu$SR) measurements which have a unique sensitivity to volume fractions of
magnetically ordered and paramagnetic regions, and studied QPTs from itinerant
heli/ferro magnet to paramagnet in MnSi (single-crystal; varying pressure) and
(Sr$_{1-x}$Ca$_{x}$)RuO$_{3}$ (ceramic specimens; varying $x$). Our results
provide the first clear evidence that both cases are associated with
spontaneous phase separation and suppression of dynamic critical behavior,
revealed a slow but dynamic character of the ``partial order'' diffuse spin
correlations in MnSi above the critical pressure, and, combined with other
known results in heavy-fermion and cuprate systems, suggest a possibility that
a majority of QPTs involve first-order transitions and/or phase separation.
