Good question. Bp Fellay has stated several times that the Pope and Ecclesia Dei have spoken to him about a kind of personal prelature, a bit like Opus Dei, where the SSPX would answer through some canonical structure to the Pope, and would not come under the jurisdiction of the local diocese. From what I heard, the Pope gave the istructions to Ecclesia Dei who were to craft the canonical structure.
Theoretically, the SSPX would continue to provide sacraments in its chapels, as it currently does worldwide, but could also offer Mass in diocesan cathedrals and other Catholic places of worship with the permission of the local ordinary.
I would also expect to see bishops and cardinals, several of whom are friendly with the SSPX, invited to offer Mass in SSPXchapels as well as perform other sacramental rites such as Confirmation and Holy Orders.
The FSSP is a priestly fraternity that falls under Ecclesia Dei and relies on local bishops to engage them to offer the EF in diocesan churches. There are some personal parishes chartered by willing diocesan bishops, which exclusively offer the EF that are staffed by the FSSP, but again, it falls under the diocese and the local bishop.
The ICK has a similar arrangement with some diocese.