  We prove in this paper that, under suitable coinditions on an initial data
set, we can obtain Area and Curvature Estimates for simple marginally outer
trapped surfaces (or MOTS). Using this estimates, we derive a Compactness
Theorem for MOTS. Moreover, the Compactness Theorem will allow us to adapt the
recent Degree Theory of H. Rosenberg and G. Smith for proving existence results
for embedded MOTS in suitable compact initial data sets
