  We investigate the dependence of the N\'eel skyrmion size and stability on
perpendicular magnetic field in ultrathin circular magnetic dots with
out-of-plane anisotropy and interfacial Dzyaloshinskii-Moriya exchange
interaction. Our results show the existence of two distinct dependencies of the
skyrmion radius on the applied field and dot size. In the case of skyrmions
stable at zero field, their radius strongly increases with the field applied
parallel to the skyrmion core until skyrmion reaches the metastability region
and this dependence slows down. More common metastable skyrmions demonstrate a
weaker increase of their size as a function of the field until some critical
field value at which these skyrmions drastically increase in size showing a
hysteretic behavior with coexistence of small and large radius skyrmions and
small energy barriers between them. The first case is also characterized by a
strong dependence of the skyrmion radius on the dot diameter, while in the
second case this dependence is very weak.
