texture ref bound to linear memory texture ref. binding limit

CUDA spec says that for a texture reference bound to linear memory, the maximum width is 2^27.
Does this maximum width mean that each texture reference can refer to a memory region whose size is up to 2&27, but it does not matter how many (memory region, texture reference) mappings exist? or does this width mean the total memory size that can be bound to texture references?

It is the width that can be bound to a particular texture reference, not an aggregate total.

There is an independent limit on the number of texture references, I believe, but it is very high.