there is a famous lemma which says: if $Y$ and $W$ are flat,projective schemes over $S$ and $s \in S$ be a geometric point and $Y_s$ and $W_s$ be fibers over $s$ and $f:Y_s \to W_s$ be a morphism then with some good conditions we have:
Dimension of every component of scheme $Hom_S(Y,W)$ at a point $f$ is at least:dim$H^0(Y_s,f^*T_{W_s})-$ dim$H^1(Y_s,f^*T_{W_s})+$ dim$S$.
Now suppose that $C$ is a nodal curve of genus zero and $\mu:C \to X$ is a stable map.Suppose that $\bar{C}$ be smoothing of $C$ over some base like $S$ and $\chi = X \times S$.
($X$ is convex,nonsingular variety)
My question is that how can we use above lemma to prove that $\mu$ lies in closure of locus of maps with irreducible domain?