  (Abridged) We present the results of three-dimensional
radiation-hydrodynamics simulations of the formation and evolution of early
HII/HeIII regions around the first stars. Cooling (by H2 and HD) and recollapse
of the gas in the relic HII region is also followed in a full cosmological
context, until second-generation stars are formed. A large HII region with a
few kiloparsec diameter is formed, within which a smaller HeIII region is
embedded. Radiative feedback effect quenches further star-formation within the
halo for a hundred million years. Accretion onto remnant blackholes will be
inefficient. Recombination radiation within the HII region is weak, but
persists for 50 million years. We also follow the thermal and chemical
evolution of the photo-ionized gas in the relic HII region. The gas cools by HD
line cooling down to a few tens Kelvin. At high redshifts (z>10), the minimum
gas temperature is limited by T_CMB. Because of its low temperature, the
characteristic mass of a Jeans-unstable gas clump is ~ 40 Msun, and is
significantly smaller than a typical clump mass for early primordial gas
clouds. We find no evidence of fragmentation by this epoch. Together with the
small cloud mass, this result indicates that massive, rather than very massive,
primordial stars may form in the relic HII region. Such stars might be
responsible for early metal-enrichment of the interstellar medium from which
recently discovered hyper metal-poor stars were born.
