  Let (C, p_1, p_2, \ldots, p_n) be a general marked curve of genus g, and q_1,
q_2, ..., q_n \in P^r be a general collection of points. We determine when
there exists a nondegenerate degree d map f : C \to P^r so that f(p_i) = q_i
for all i. This is a consequence of our main theorem, which states that the
restricted tangent bundle f^* T_{P^r} of a general curve of genus g, equipped
with a general degree d map f to P^r, satisfies the property of interpolation
(i.e.\ that for a general effective divisor D of any degree on C, either
H^0(f^* T_{P^r}(-D)) = 0 or H^1(f^* T_{P^r}(-D)) = 0). We also prove an
analogous theorem for the twist f^* T_{P^r}(-1).
