  We consider static electrically charged dust configurations in the framework
of Einstein-Maxwell-dilaton gravity with the interaction term P(\chi) F_{mn}
F^{mn} in the Lagrangian, where P(\chi) is an arbitrary function of the dilaton
field \chi, and the latter is allowed to be normal or phantom. It is shown
that, for any regular P(\chi), static configurations are possible with
arbitrary functions g_{00} = e^{2\gamma(x^i)} (i=1,2,3) and \chi =
\chi(\gamma), without any assumption of spatial symmetry. The corresponding
matter, electric charge and scalar charge densities are found from the field
equations. Meanwhile, configurations with nontrivial \chi(x^i) generically
require a nonzero scalar charge density distribution. The classical
Majumdar-Papapetrou (MP) system is obtained as a special case where \chi =
const; there is its scalar analogue in the case F_{mn} = 0, but only with a
phantom \chi field. Among possible solutions are black-hole (BH) and
quasi-black-hole (QBH) ones. Some general results on QBH properties obtained
previously for the MP system are here extended to systems with the dilaton.
Particular examples of asymptotically flat spherically symmetric BH and QBH
solutions are found, some of them being phantom-free, that is, exist with
positive energy densities of matter and both scalar and electromagnetic fields.
