BV analysis of Polyakov and Nambu-Goto theories with boundary

The Batalin-Vilkovisky data for Polyakov string theory on a manifold with (non-null) boundary is shown to induce compatible Batalin--Fradkin--Vilkovisky data, thus allowing BV-quantisation on manifolds with boundary. On the other hand, the analogous formulation of Nambu--Goto string theory fails to satisfy the needed regularity requirements. As a byproduct, a concise description is given of the reduced phase spaces of both models and their relation, for any target $d$-dimensional Lorentzian manifold.