  We present results of computer simulations of a parahydrogen cluster of a
thousand molecules, corresponding to approximately 4 nm in diameter, at
temperatures between 1 K and 10 K. Examination of structural properties
suggests that the local environment experienced by molecules is very similar to
that in solid bulk parahydrogen, especially near the center of the cluster,
where crystallization originates. Albeit strongly suppressed compared to
helium, quantum-mechanical exchanges are not entirely negligible at the lowest
temperature, resulting in a small but significant molecular mobility
enhancement with respect to the bulk crystalline phase. Although the overall
superfluid response at the lowest temperature is only a few percents, there is
evidence of a surprising "supersolid" core, as well as of a superfluid outer
shell. Much like in fluid parahydrogen at the melting temperature,
quantum-mechanical signatures can be detected in the momentum distribution.
