For a link L, the splitting number is the minimum number of crossing changes required to change the link into a split link, where all crossing changes must be between different components. The minimum is taken over all diagrams of the link.
For links of 9 or fewer crossings, the final complete tabulation was given in [2]. For earlier results and progress on higher crossing links, see [1] and [3].
References
[1] Batson, J. and Seed, C. A link splitting spectral sequence in Khovanov homology, http://arxiv.org/abs/1303.6240, 2013.
[2] Cha, J.-C., Friedl, S., and Powell, M. Splitting numbers of links, http://arxiv.org/abs/1308.5638, 2013.
[3] Kohn, P. Unlinking two component links, Osaka J. Math. 30 (1993), 741752.