PBTH Agreements, originally referred to engine lease/maintenance deals, but now is often used in reference to airframes, engines, components and support functions. Engine deals do not always involve leaseing in engines, quite often the operator will still own the engines, but pay a fixed cost per flying hour to the engine agency in lieu of any shop visit costs.
The principal of PBTH is very sound and is often beneficial to the smaller operators, who wish to reduce financial risks. However the crucial part is the detail of the deal and the organisation that the opertaor chooses to enter into the agreement with.
PBTH deals are often signed over two or more years, to acheive real financial benefit, and over that time the perfomance of the provider could vary. There's nothing worse than an airline with a grounded aircraft and no engine to install. Do you then expend countless resources suing the agency for breach of contract or purchase/lease your own engine. either way your going down finacial routes that you were trying to avoid.
The prinipal of PBTH is a sound one providing the contract is well constructed and the service provider is reputable.
I hope this and the other replies go some way to answering the question.