  In this article we study the asymptotic behavior of anisotropic nonlocal
nonstandard growth seminorms and modulars as the fractional parameter goes to
1. This gives a so-called Bourgain-Brezis-Mironescu type formula for a very
general family of functionals. In the particu\-lar case of fractional Sobolev
spaces with variable exponent, we point out that our proof asks for a weaker
regularity of the exponent than the considered in previous articles.
