  Let S be an arbitrary real surface, with or without boundary, contained in a
hypersurface M of the complex euclidean space \C^2, with S and M of class C^{2,
a}, where 0 < a < 1. If M is globally minimal, if S is totally real except at
finitely many complex tangencies which are hyperbolic in the sense of E. Bishop
and if the union of separatrices is a tree of curves without cycles, we show
that every compact K of S is CR-, W- and L^p-removable (Theorem~1.3). We treat
this seemingly global problem by means of purely local techniques, namely by
means of families of small analytic discs partially attached to maximally real
submanifolds of C^n and by means of a thorough study of the relative
disposition of the characteristic foliation with respect to the track on M of a
certain half-wedge attached to M. This localization procedure enables us to
answer an open problem raised by B. J\"oricke: under a certain
nontransversality condition with respect to the characteristic foliation, we
show that every closed subset C of a C^{2,a}-smooth maximally real submanifold
M^1 of a (n-1)-codimensional generic C^{2,a}-smooth submanifold of \C^n is CR-,
W- and L^p-removable (Theorem~1.2'). The known removability results in CR
dimension at least two appear to be logical consequences of Theorem~1.2'. The
main proof (65p.) is written directly in arbitrary codimension. Finally, we
produce an example of a nonremovable 2-torus contained in a maximally real
3-dimensional maximally real submanifold, showing that the nontransversality
condition is optimal for universal removability. Numerous figures are included
to help readers who are not insiders of higher codimensional geometry.
