I believe that an SI is more likely to arise spontaneously than by
design.
Even if the SI arises by design, I don't believe that that its initial
design
will profoundly influence its ultimate characteristics, since it will
take
control of its own development.
There is actually a reasonable secnario that would limit an SI to one
star system
but stil make it use up all the resources in that start system. This
will occur if the SI is attempting to maximize is computational speed
and capacity until it achieves some breakthrough that causes it to no
longer have this maximization
as a goal. The payback time for using out-of-system resources is very
long, since
the mass you send out-of-system can otherwise be used to augment your
in-system resources with no speed-of-light delay. Thus, the SI must
choose between immedate use of the mass to build more local computing
capacity, or investingthe mass in a mission to another system to return
more computing capacity later. I feel that the SI may choose to keep the
mass, since at the SI's speed of computation, the return of resources
from another system is an incredibly large number of computational
cycles into the future.
One technique that an SI may use to speed itself up is to convert itself
into
a neutron star. This puts the mass in a smaller radius, which increases
the
computing capacity by reducing signalling delays.