What is the meaning of 相邻权？ I know nothing at all about the law, so I don't know how 相邻权 might be translated in English. ‘neighbours law' doesn't seem very jurisprudent! Any tips please?

近年知识产权案件逐年上升，案件类型也从单纯的著作权，商标权和专利权向其相邻权转变，案件涉及的领域也更加广泛。

After a few rereads, I come to the conlusion '向其相邻权‘ is not a law or a right, it just means '(and) to their related laws' Is that right? I'm a bit slow off the mark this morning!
著作权的"相邻权" is not 'related laws' but 'related rights'. Related laws is 相关的法律。It is not the same as 相邻权 of real estates. I think the Chinese term might be a bit hard to understand, because 相邻 means adjacency not related. 

Chinese definition

著作权(知识产权)的相邻权或邻接权，是表演者、录音录像制作者和广播企业对其节目、录音录像制品所拥有的权利，这一权利主要通过1961年10月26日的《关于表演者、唱片制作者和广播组织的国际公约》(罗马公约)， 1971年10月29日的《保护唱片制作者防止唱片被擅自复制公约》(唱片公约) 以及1996年12月20日由世界知识产权组织制定的《表演和录音制品条约》进行调整。

English explanation

The purpose of related rights is to protect the legal interests of certain persons and legal entities who contribute to making works available to the public; or who produce subject matter which, while not qualifying as works under the copyright systems of all countries, contain sufficient creativity or technical and organizational skill to justify recognition of a copyright-like property right.

From http://www.wipo.int/edocs/pubdocs/en/intproperty/909/wipo_pub_909.pdf (Page 16)