  To avoid the complicated topology of surviving clusters induced by standard
Strong Disorder RG in dimension $d>1$, we introduce a modified procedure called
'Boundary Strong Disorder RG' where the order of decimations is chosen a
priori. We apply numerically this modified procedure to the Random Transverse
Field Ising model in dimension $d=2$. We find that the location of the critical
point, the activated exponent $\psi \simeq 0.5$ of the Infinite Disorder
scaling, and the finite-size correlation exponent $\nu_{FS} \simeq 1.3$ are
compatible with the values obtained previously by standard Strong Disorder
RG.Our conclusion is thus that Strong Disorder RG is very robust with respect
to changes in the order of decimations. In addition, we analyze in more details
the RG flows within the two phases to show explicitly the presence of various
correlation length exponents : we measure the typical correlation exponent
$\nu_{typ} \simeq 0.64$ in the disordered phase (this value is very close to
the correlation exponent $\nu^Q_{pure}(d=2) \simeq 0.63$ of the {\it pure}
two-dimensional quantum Ising Model), and the typical exponent $\nu_h \simeq 1$
within the ordered phase. These values satisfy the relations between critical
exponents imposed by the expected finite-size scaling properties at Infinite
Disorder critical points. Within the disordered phase, we also measure the
fluctuation exponent $\omega \simeq 0.35$ which is compatible with the Directed
Polymer exponent $\omega_{DP}(1+1)=1/3$ in $(1+1)$ dimensions.
