  We study the approximation of J-holomorphic maps continuous to the boundary
from ma domain in the complex plane into an almost complex manifold by maps
J-holomorphic to the boundary, giving partial results in the non-integrable
case. For the integrable case, we study arcs in complex manifolds and establish
the existence of neighborhoods biholomorphic to open sets in Euclidean space
for several classes of arcs. As an application, we obtain $\mathcal{C}^k$
approximation of holomorphic maps continuous to the boundary into complex
manifolds by maps holomorphic to the boundary, provided the boundary is nice
enough.
