  The spatial distribution of the Ly$\alpha$ forest is studied using new HST
data for the quasar pair Q~1026--0045 A and B at $z_{em}$ = 1.438 and 1.520
respectively. The angular separation is 36 arcsec and corresponds to transverse
linear separations between lines of sight of $\sim300h^{-1}_{50}$ kpc ($q_{o}$
= 0.5) over the redshift range 0.833 < z < 1.438. From the observed numbers of
coincident and anti-coincident Ly$\alpha$ absorption lines, we conclude that,
at this redshift, the Ly$\alpha$ structures have typical dimensions of
$\sim500h^{-1}_{50}$ kpc, larger than the mean separation of the two lines of
sight. The velocity difference, $\Delta V$, between coincident lines is
surprisingly small (4 and 8 pairs with $\Delta V < 50 and 200 km/s
respectively).
  Metal line systems are present at $z_{abs}$ = 1.2651 and 1.2969 in A,
$z_{abs}$ = 0.6320, 0.7090, 1.2651 and 1.4844 in B. In addition we tentatively
identify a weak Mg II system at $z_{abs}$ = 0.11 in B. It is remarkable that
the $z_{abs}$ = 1.2651 system is common to both lines of sight. The system at
$z_{abs}$ = 1.4844 %is probably associated and has strong O~VI absorption.
  There is a metal-poor associated system at $z_{abs}$ = 1.4420 along the line
of sight to A with complex velocity profile. We detect a strong Ly$\alpha$
absorption along the line of sight to B redshifted by only 300 km/s relatively
to the associated system. It is tempting to interpret this as the presence of a
disk of radius larger than 300$h^{-1}_{50}$ kpc surrounding quasar A.
