  The cosmic no hair conjecture is tested in the spherically symmetric
Einstein-Maxwell-dilaton~(EMD) system with a positive cosmological constant
$\Lambda$. Firstly, we analytically show that once gravitational collapse
occurs in the massless dilaton case, the system of field equations breaks down
inevitably in outer communicating regions or at the boundary provided that a
future null infinity ${\cal I}^+$ exists. Next we find numerically the static
black hole solutions in the massive dilaton case and investigate their
properties for comparison with the massless case. It is shown that their
Abbott-Deser~(AD) mass are infinite, which implies that a spacetime with finite
AD mass does not approach a black hole solution after the gravitational
collapse. These results suggest that ${\cal I}^+$ cannot appear in the EMD
system once gravitational collapse occurs and hence the cosmic no hair
conjecture is violated in both the massless and the massive cases, in contrast
to general relativity.
