Yours is a layered question :). So let me pick out the key elements:
Taxonomy as you say- T&M, MS, Fixed Price etc
This is not specific to Spain or Europe, but used world over by organisations depending on the type of project, resourcing, cost, budget & quality requirements
This is typically used when its diffcult to accurately nail the scope of the project or the client just wants resources (think bodyshopping/bums on seats) to fill gaps. There are pros & cons to this, and personally I have not come across any research or PoV to suggest that over time this will be more in demand. I am happy to help you with detail of this if you are keen as this is huge subject in itself. But there is plenty of material online on this
Drivers for T&M
- Skills gaps that organisaiton cant fill themselves or immediate hiring
- Scope of project can change over time, so a billing by day & effort model works
- Client/organisation willing to take on more risk
- Timelines are short and some work needs to be done quickly
World of IT is shifting to agile (it will never be 100% agile though), gone are the days where organisations will wait many weeks/months before a project starts to deliver value. Getting something (a minimum viable product) quickly and improving it is Agile. Then if you make a mistake, you can course correct quickly via the sprints.
I am personally seeing a lot of T&M Agile contracts and also Fixed-Price Agile contracts in the industry.
Manages Services kicks in once deployment is complete and the organisation needs maintenance, support, continuous improvement. Typically all large IT projects will have MS built it for a certain duration.
There isnt a one size fits all approach as IT is a complex domain.
Happy to help more so feel free to shoot me direct message.