Transverse mode-coupling instability (TMCI) is known to limit bunch intensity by exciting exponential growth of bunch transverse oscillations. Since space charge (SC) generally changes coherent spectra, it affects the TMCI threshold. Generally, there are only two types of TMCI with respect to SC: vanishing type and strong space charge (SSC) type. For the former, threshold value of the wake tune shift is asymptotically proportional to the SC tune shift, as it was first observed 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 for cosine wakes. In our studies of various wakes, potential wells, and bunch distributions, presented in this paper, the second type of instability was, indeed, always seen for cosine wakes; it was also seen for sine wakes in case of a bunch within a square potential well. The vanishing TMCI was found 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. As an especially interesting example, at the end of this paper, we consider high-frequency broadband wake, suggested for CERN SPS ring; as expected, TMCI is of the vanishing type in this case. Certain contradictions between results of our SSC analytical approach and ones of macroparticle simulations are discussed.