  We prove that every smooth subelliptic variety admits a surjective morphism
from an affine space. This result gives partial answers to the questions of
Arzhantsev and Forstneri\v{c}. As an application, we characterize open images
of morphisms between affine spaces. We also obtain the jet interpolation
theorem for morphisms from zero-dimensional subschemes of affine varieties to
smooth subelliptic varieties.
