  We study the branching ratios of rare K and B decays in models with minimal
flavour violation, using the presently available information from the universal
unitarity triangle analysis and from the measurements of Br(B -> X_s gamma),
Br(B -> X_s l^+l^-) and Br(K^+ -> pi^+ nu nubar). We find the following upper
bounds: Br(K^+ -> pi^+ nu nubar)< 11.9 10^{-11}, Br(K_L -> pi^0 nu nubar)< 4.6
10^{-11}, Br(K_L -> mu mubar)_{SD}< 1.4 10^{-9}, Br(B -> X_s nu nubar)< 5.2
10^{-5}, Br(B -> X_d nu nubar)< 2.2 10^{-6}, Br(B_s -> mu mubar)< 7.4 10^{-9},
Br(B_d -> mu mubar)< 2.2 10^{-10} at 95 % probability. We analyze in detail
various possible scenarios with positive or negative interference of Standard
Model and New Physics contributions, and show how an improvement of
experimental data corresponding to the projected 2010 B factory integrated
luminosities will allow to disentangle and test these different possibilities.
Finally, anticipating that subsequently the leading role in constraining this
kind of new physics will be taken over by the rare decays K^+ -> pi^+ nu nubar,
K_L -> pi^0 nu nubar and B_{s,d} -> mu mubar, that are dominated by the Z^0
-penguin function C, we also present plots for several branching ratios as
functions of C . We point out an interesting triple correlation between K^+ ->
pi^+ nu nubar, B -> X_s gamma and B -> X_s l^+l^- present in MFV models.
