If you pay an advertising agency to create an advert for you, who owns the intellectual property rights in the advert? The advertiser or the agency?

It's advertiser's right's. The brief usually gave by the advertiser and the agency get paid for the serv ice provided. Agency benefits with all the accolades it receives when the creatives really serve the objective. And at times vice-versa.

In normal cases its advertiser, until there's any special agreement about the intellectual rights...