The SuperEMFL is a project aimed at designing high-field magnets for users in Europe. The core of the project is the complete design of two full SC magnets, made of a HTS insert and a LTS outsert: first, a 32 T magnet design, extension of the NOUGAT insert into a LTS magnet outsert (in place of the resistive outsert coils), with a large usable cold bore of 50 mm diameter, second, a 40 T or more magnet design, with a smaller cold bore around 25 mm diameter.

We present here the main outcomes from the studies led during the 4 year length of the project: development of dedicated tools to calculate quench dynamics in HTS, protection and mechanical studies taking into account the strong interactions between HTS and LTS parts and final designs.