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We investigate the rest-frame UV morphologies of a large sample of Lyman-aemitters (LAEs) from z~2 to z~6, selected in a uniform way with 16 differentnarrow- and medium-bands over the full COSMOS field. We use 3045 LAEs with HSTcoverage in a stacking analysis and find that they have M_UV~-20, below M*_UVat these redshifts. We also focus our analysis on a subsample of 780 individualgalaxies with i_AB<25 for which GALFIT converges for 429 of them. Theindividual median size (re~1 kpc), ellipticities (slightly elongated with(b/a)~0.45), S\'ersic index (disk-like with n<2) and light concentration(comparable to that of disk or irregular galaxies, with C~2.7) of LAEs showmild evolution from z~2 to z~6. LAEs with the highest rest-frame equivalentwidths (EW) are the smallest/most compact (re~0.8 kpc, compared to re~1.5 kpcfor the lower EW LAEs). When stacking our samples in bins of fixed Lyaluminosity and Lya EW we find evidence for redshift evolution in n and C, butnot in galaxy sizes. The evolution seems to be stronger for LAEs with 25<EW<100{\AA}. When compared to other SFGs, LAEs are found to be smaller at allredshifts. The difference between the two populations changes with redshift,from a factor of ~1 at z>5 to SFGs being a factor of ~2-4 larger than LAEs forz<2. This means that at the highest redshifts, where typical sizes approachthose of LAEs, the fraction of galaxies showing Lya in emission (and with ahigh Lya escape fraction) should be much higher, consistent with observations.

On the UV compactness and morphologies of typical Lyman-a emitters from z~2 to z~6