  We consider how changes in transfinite machine architecture can sometimes
alter substantially their capabilities. We approach the subject by answering
three open problems touching on: firstly differing halting time considerations
for machines with multiple as opposed to single heads, secondly space
requirements, and lastly limit rules. We: 1) use admissibility theory,
$\Sigma_{2}$-codes and $\Pi_{3}$-reflection properties in the constructible
hierarchy to classify the halting times of ITTMs with multiple independent
heads; the same for Ordinal Turing Machines which have $\tmop{On}$ length
tapes; 2) determine which admissible lengths of tapes for transfinite time
machines with long tapes allow the machine to address each of their cells - a
question raised by B. Rin; 3) characterise exactly the strength and behaviour
of transfinitely acting Blum-Shub-Smale machines using a $\tmop{Liminf}$ rule
on their registers - thereby establishing there is a universal such machine.
This is in contradistinction to the machine using a `continuity' rule which
fails to be universal.
