Tenerife estate agents are known as inmobiliaria. There are still many here servicing clients from the UK though quite a few folded at the beginning of the economic crash.
When buying property anywhere in Spain you are better to enlist the services of a professional. Debts are transferred with the property. An experienced agent will ensure that there are no such problems attached to your new dream home in the sun.
Similarly, if you recall recently there have been quite a few cases in mainland Spain where beutiful properties have been bulldozed to the ground leaving their owners in tears amid the rubble. Dodgy planning permission is usually to blame (and greedy councillors).
A professional agent knows which land is allotted for building purposes and which is not. He or she will steer you clear of anything that looks less than 100% legitimate. (or at the very least tell you what you are risking should there be a crackdown of illegal buildings in Tenerife in the near future).
The little amount of money you might save on the estate agents fees is really a false economy unless you know exactly what you are doing.