Who owns the laptop bought with funding for student training etc. in a fully funded PhD project?
If it isn't specified in the collaboration contract, ask the funding agency for clarification - this may be determined on a case-to-case basis.



Single data point: I had funding as PhD student via a sholarship that also had an expenses budget.


When I bought stuff that was in between consumables and small instruments (to be precise, VUV-quality CaF2 slides). At reimbursement, the funding agency stipulated that they should become property of the institute. 
In contrast, there was no such stipulation for some books I bought from the same budget.