In Spain, number plates always follow the vehicle.

It is very important to be aware that any outstanding car debts belonging to the former owner follow the vehicle.  This means that if the car is paid for by credit and there are still X monthly payments outstanding, the 'car' owes the debt. You must make sure that at the time of purchase, there are no outstanding debts on the car.  If credit payments are still due you will be liable to pay those amounts.
The first thing is to make out a contract of purchase and sale; one original for the seller and one original for the buyer.
Together with the seller, you must also fill in Model 9.050 (paperwork) which gives you the authorization to change the car into your name.  Do not forget to ask the seller for copies of his passport or identity card and NIE.
Good advice: make several copies of all your documents. The various administrations that you will be dealing with all require copies and and don’t offer an in-house “copy service”.
Go to the Oficina Tributaria (or SAC – “Service de Atención al Ciudadano”) to pay the registration fee (Impuesto de Transmisiones).  Carry all car documents  - the Permiso de Circulacíon,  car Inspection papers (ITV) in the car. You will pay more or less 4% of the declared value of the car.  You will then receive your model 620 completed and signed,
With all these documents go to “Jefatura Provincial de Tráfico“ in Santa Cruz de Tenerife.
You’ll pay more or less 50€ and receive the documents in your name.
REMEMBER : Check that the seller has paid the road tax to date (Impuesto Vehiculos Tracción Mecánica) and don’t forget to take out a good car insurance.
No stress, if you want, we can arrange it for you.

Expertos de Tenerife S.L.   www.experten.es