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, Σ 2 -codes and Π 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 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 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.