Relocation disputes (also known as 'leave to remove' cases, 'removal from the jurisdiction' cases or, in North America, 'move-away cases') are usually in the latter category. These are cases which arise when one parent proposes to move to a new geographic location and take their child or children with them. These cases often involve proposals to move to a different country, though they might also be about moves within the UK. Even quite short moves can be disputed sometimes (see E v E  EWCA Civ 843, where the move in question would have been just over an hour's drive), though these cases usually settle long before the court gets invovled.
There are many complications to relocation law, and many commentators inside and outside the legal professions have strongly-held views. I have been researching in this area for about 6 years now, and I still find angles that I hadn't thought of before and questions that I can't answer. One difficulty is that both parties to the relocation dispute have good arguments to support their positions, and it is hard to think that one of them automatically has the better of the argument.
The parent seeking to move (usually but by no means always the mother) can say that she is entitled to live her own life and not be tied to her former partner for the rest of her life. She is often wanting to leave to the UK to return to her original home country, often seeking support from her wider family in bringing up the children. She might have a new partner who needs or wants to move - maybe for work, for family, or simply to go in search of a better life. From an equality point of view, it can also be noted that parents who are not performing the main care-giving function in their children's lives are free to move as and when they like, regardless of any impact on the children or other parent.
On the other side, the parent opposing the relocation (usually but not always the father) can fairly point out that his relationship with his children is also important for their wellbeing and upbringing, and that he will be sidelined in their lives if they move away. A weekly chat on Skype is hardly going to fill the gap left by a day spent together every week (and in fact the non-moving parents in relocation disputes are often seeing their children far more often than this). Moving to a new country is often disruptive for children in terms of schooling, and if the country in question is culturally very different from the UK then some children struggle to settle.
There is lots that we know about relocation disputes in the family courts, but far more that we don't. The family courts in this country keep especially poor administrative data about their cases, which means that we do not know some incredibly basic information. Things like: how many relocation cases are litigated every year. Or how many relocation applications are allowed and how many are refused. Or how many cases are brough by mothers, how many by fathers, and how many by other family members. Or how old the children are, on average, in a relocation case.
For anyone interested in reforming the law - and there are many people who think that relocation law in this country should be looked at again - this lack of information is a real problem (though they don't always seem to realise it!). How can we know whether the allegation that the law is biased in favour of relocation is true or not when we don't even know how many applications are granted?
There are lots of ways that research could help to answer these problems. One approach, which the British Academy is funding me to try, is to gather as many family court decisions in relocation cases as possible over a 12-month time-frame. All the family court judges in England and Wales have been asked to send in copies of the judgments and orders that they make during 2012 to me to analyse. The going is quite slow so far - just 6 or 8 cases per month have arrived so far - but it is hard to know how successful the research is becuase we don't know how many cases there actually are! (The first question you want to ask as a scientist is about response rate, but this research can never answer that question - I don't know whether there really were only 8 cases in January 2012 and I got them all, or whether there were 80 and I got only 10%.)
Anyway, only time will tell - but the need for relocation law is not going to go anywhere any time soon. Migration rates are increasing every year and, as people increasingly share the care of children in post-separation parenting arrangements, the arguments about proposed relocations are surely going to become more frequent too. The more we can learn about these cases, the better equipped we will be to know how best to resolve them.
Further details about my research project and publications can be found on my Faculty webpage.