  Given a manifold with boundary, one can consider the space of subsurfaces of
this manifold meeting the boundary in a prescribed fashion. It is known that
these spaces of subsurfaces satisfy homological stability if the manifold has
at least dimension five and is simply-connected. We introduce a notion of
tangential structure for subsurfaces and give a general criterion for when the
space of subsurfaces with tangential structure satisfies homological stability
provided that the manifold is simply-connected and has dimension $n\geq 5$.
Examples of tangential structures such that the spaces of subsurface with that
tangential structure satisfy homological stability are framings or spin
structures of their tangent bundle, or $k$-frames of the normal bundle provided
that $k\leq n-2$.
  Furthermore we introduce spaces of pointedly embedded subsurfaces and
construct stabilization maps, as well as prove homological stability for these.
This is used to prove homological stability for spaces of symplectic
subsurfaces.
