  Transverse mode-coupling instability (TMCI) is known to limit bunch
intensity. Since space charge (SC) changes coherent spectra, it affects the
TMCI threshold. Generally, there are only two types of TMCI with respect to SC:
the vanishing type and the strong space charge (SSC) type. For the former, the
threshold value of the wake tune shift is asymptotically proportional to the SC
tune shift, as it was first observed twenty years ago by M. Blaskiewicz for
exponential wakes. For the latter, the threshold value of the wake tune shift
is asymptotically inversely proportional to the SC, as it was shown by one of
the authors. In the presented studies of various wakes, potential wells, and
bunch distributions, the second type of instability was always observed for
cosine wakes; it was also seen for the sine wakes in the case of a bunch within
a square potential well. The vanishing TMCI was observed for all other wakes
and distributions we discuss in this paper: always for the negative wakes, and
always, except the cosine wake, for parabolic potential wells. At the end of
this paper, we consider high-frequency broadband wake, suggested as a model
impedance for CERN SPS ring. As expected, TMCI is of the vanishing type in this
case. Thus, SPS Q26 instability, observed at strong SC almost with the same
bunch parameters as it would be observed without SC, cannot be TMCI.
