  We carry out a systematic study of exotic $QQ^\prime \bar q\bar q$ four-quark
states containing distinguishable heavy flavors, $b$ and $c$. Different generic
constituent models are explored in an attempt to extract general conclusions.
The results are robust, predicting the same sets of quantum numbers as the best
candidates to lodge bound states independently of the model used, the isoscalar
$J^P=0^+$ and $J^P=1^+$ states. The first state would be strong and
electromagnetic-interaction stable while the second would decay
electromagnetically to $\bar B D \gamma$. Isovector states are found to be
unbound, preventing the existence of charged partners. The interest on exotic
heavy-light tetraquarks with non identical heavy-flavors comes reinforced by
the recent estimation of the production rate of the isoscalar $bc\bar u \bar d$
$J^P=1^+$ state, two orders of magnitude larger than that of the $bb\bar u\bar
d$ analogous state.
