Has anyone ever heard of a geared turbofan in which the axis of rotation of the fan is offset from (i.e. not the same as) the axis of rotation of the turbine? In all the current geared turbofans I've encountered, the input shaft from the turbine to the gearbox is co-axial with the output shaft to the fan.
There are no off-centered turbofan engines in service today. However, United Technologies Corporation (UTC), has patented an engine with an angled core (Pratt & Whitney is a part of UTC).
Image from US patent Gas turbine engine with separate core and propulsion unit US 8789354 B2
Air from the fan is ducted around the side and back of the core to enter from the opposite direction. The hot gas will be discharged forward through a power (low-pressure) turbine connected to the fan via a gear system. The turbine, gearbox and fan will be connected through a short shaft.
The design is expected to have some advantages due the unconventional layout adopted, like:
As the core and fan are separate, core can be easily removed for maintenance.
As the compressors (in cores) are at an angle to each other, the possibility that uncontained failure in one engine will damage another engine is reduced (when the engines are installed in the double bubble D8 configuration)