In recent years, much progress has been made on the structure of fundamental groups of algebraic curves by means of patching techniques in formal and rigid geometry. A number of these results have concerned curves over algebraically closed fields of characteristic p — e.g. the proofs of the Abhyankar Conjecture ([Ra], [Ha5]) and of the geometric case of the Shafarevich Conjecture ([Po1], [Ha6]), and the realization of Galois groups over projective curves ([Sa1], [St1]). While the rigid approach to patching is often regarded as more intuitive than the formal approach, its foundations are less well established. But constructions involving the formal approach have tended to be technically more cumbersome. The purpose of the current paper is to build on previous formal patching results in order to create a framework in which such constructions are facilitated. In the process we prove a result asserting that singular curves over a field k can be thickened to curves over k[[t]] with prescribed behavior in a formal neighborhood of the singular locus, and similarly for covers of curves. Afterwards, we obtain applications to fundamental groups of curves over large fields. The structure of the paper is as follows: Section 1 concerns patching problems for projective curves X∗ over a power series ring R = k[[t1, . . . , tn]]. It is shown (Theorem 1) that giving a coherent projective module over X is equivalent to giving such modules compatibly on a formal neighborhood of each singular point of the closed fibre X , and on the formal thickening along the complement of the singular locus S of X . Section 2 applies this to thickening problems, in both the absolute and relative senses. Namely, it shows (Theorem 3) that such an X∗ can be constructed from its closed fibre X and from complete local thickenings near S, such that X∗ is a trivial deformation away from S. Moreover (Theorem 2), given a morphism X → Z and a thickening Z∗ of Z, such that the local thickenings near S are compatible with that of Z, there is a unique such thickening X∗ of X that is compatible with the given data. In Section 3 these results are applied to the problem of thickening and deforming covers. Theorem 4 there combines the results of Sections 1 and 2 to show that covers of reducible k-curves can be thickened to covers of curves over k[[t]], and Theorem 5 then shows how this can be used over large fields to