  Let $\{u_n\}$ be a sequence of maps from a compact Riemann surface $M$ with
smooth boundary to a general compact Riemannian manifold $N$ with free boundary
on a smooth submanifold $K\subset N$ satisfying \[ \sup_n \ \left(\|\nabla
u_n\|_{L^2(M)}+\|\tau(u_n)\|_{L^2(M)}\right)\leq \Lambda, \] where $\tau(u_n)$
is the tension field of the map $u_n$. We show that the energy identity and the
no neck property hold during a blow-up process. The assumptions are such that
this result also applies to the harmonic map heat flow with free boundary, to
prove the energy identity at finite singular time as well as at infinity time.
Also, the no neck property holds at infinity time.
