Let $k$ be a field, let $X/k$ be a nodal curve (which means $X\_{\overline{k}}$ is a connected reduced proper curve with at worst nodal singularities.)


Does there always exists a proper flat family $\mathcal{X}/\mathrm{Spec}(k[[t]])$ with special fiber $X$ and smooth generic fiber? (Is there a reference for this?)



Smoothen a nodal curve
Yes. One reference I know is Brian Conrad's appendix to Matt Baker's paper, "[Specialization of linear systems from curves to graphs](https://projecteuclid.org/euclid.ant/1513797305)". See, in particular, Theorem B.2 therein.


