  The phase diagram of unzipping of an adsorbed directed polymer in two
dimensions in a random medium has been determined. Both the hard-wall and the
soft-wall cases are considered. Exact solutions for the pure problem with
different affinities on the two sides are given. The results obtained by the
numerical procedure adopted here are shown to agree with the exact results for
the pure case. The characteristic exponents for unzipping for the random
problem are different from the pure case. The distribution functions for the
unzipped length, first bubble, and the spacer are determined.
