To be pedantic, nobody can ever own a 'boundary', since it's just an invisible line. I assume that your post refers to a 'boundary feature', such as a fence or hedge.
You need to read the text on the deeds to find out what the 'T' means. It can indicate ownership OR a covenant to maintain that feature (irrespective of whether it's owned or not) OR both.
Unless there's a covenant requiring you to maintain a boundary feature, there's no requirement that you should so, even if you own it. For example, if you own a boundary fence you can let it fall down or simply remove it. If your neighbour complains, you can simply to say to him: "If you want a fence, you provide it".
However, as indicated above, you can sometimes be required (under a covenant) to maintain a feature which you don't own. For example the deeds to my house require me to mow an area of lawn which is around the corner from my house (and which I don't own). Fortunately, the guy around the corner seems to be unaware of this ;-)
Chris