  Top flavour-changing neutral decays are extremely suppressed within the
Standard Model (SM) by the GIM mechanism, but can reach observable rates in
some of its extensions. We compute the branching ratios for t -> c gamma and t
-> c g in minimal SM extensions where the addition of a vector-like up or down
quark singlet breaks the unitarity of the 3 x 3 Cabibbo-Kobayashi-Maskawa (CKM)
matrix. The maximum rates obtained indicate to what extent present experimental
data allow 3 x 3 CKM unitarity to be broken in these models, and are too small
to be observed in the near future. As a by-product, we reproduce the
calculation of these branching ratios in the SM, and with an improved set of
parameters we obtain values one order of magnitude smaller than the ones
usually quoted in the literature. We study the CP asymmetries between the decay
rates of the top quark and antiquark, which can be much larger than in the SM,
also as a consequence of the partial breaking of 3 x 3 CKM unitarity.
