[abridged] We study the dependence of the galaxy size evolution on morphology, stellar mass and large scale environment for a sample of 298 group and 384 field quiescent early-type galaxies from the COSMOS survey, selected from z~1 to the present, and with masses $log(M/M_odot)>10.5$. The galaxy size growth depends on galaxy mass and early-type galaxy morphology, e.g., elliptical galaxies evolve differently than lenticular galaxies. At the low mass end -$10.5<Log(M/M_odot)<11$, ellipticals do not show strong size growth from $zsim1$ to the present (10% to 30% depending on the morphological classification). On the other end, massive ellipticals -log(M/M_odot)>11.2$- approximately doubled their size. Interestingly, lenticular galaxies display different behavior: they appear more compact on average and they do show a size growth of sim60% since z=1 independent of stellar mass. We compare our results with state-of-the art semi-analytic models. While major and minor mergers can account for most of the galaxy size growth, we find that with present data and the theoretical uncertainties in the modeling we cannot state clear evidence favoring either merger or mass loss via quasar and/or stellar winds as the primary mechanism driving the evolution. The galaxy mass--size relation and the size growth do not depend on environment in the halo mass range explored in this work (field to group mass $log(M_h/M_odot)<14$), i.e., group and field galaxies follow the same trends, which is at variance with predictions from current hierarchical models that show a clear dependence of size growth on halo mass for massive ellipticals -$log(M_*/M_odot)>11.2$.
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