  We address a number of unanswered questions in the N=(0,2)-deformed CP(N-1)
model with twisted masses. In particular, we complete the program of solving
CP(N-1) model with twisted masses in the large-N limit. In hep-th/0512153
nonsupersymmetric version of the model with the Z_N symmetric twisted masses
was analyzed in the framework of Witten's method. In arXiv:0803.0698 this
analysis was extended: the large-N solution of the heterotic N=(0,2) CP(N-1)
model with no twisted masses was found. Here we solve this model with the
twisted masses switched on. Dynamical scenarios at large and small m are
studied (m is the twisted mass scale). We found three distinct phases and two
phase transitions on the m plane. Two phases with the spontaneously broken
Z_N-symmetry are separated by a phase with unbroken Z_N. This latter phase is
characterized by a unique vacuum and confinement of all U(1) charged fields
("quarks"). In the broken phases (one of them is at strong coupling) there are
N degenerate vacua and no confinement, similarly to the situation in the
N=(2,2) model. Supersymmetry is spontaneously broken everywhere except a circle
|m|=\Lambda in the Z_N-unbroken phase. Related issues are considered. In
particular, we discuss the mirror representation for the heterotic model in a
certain limiting case.
