The most common case is parallel waves. For a Split Circulate, to get to the next spot in their circulate path, the leaders in each half of each wave flip over into the other spot in their own half of the wave. The trailers simply walk forward without turning, into the spot in front of them.
No dancer "crosses the center line". From right-handed waves, all of the leaders will be flipping over to their right. From left-handed waves all of the leaders will be flipping over to their left.
Split Circulate can also be done in columns. The leaders in each box flip over into the spot next to them. For the first dancer in each column, this is the same as for a Column Circulate. But the third dancer in each column must flip over into the adjacent spot, instead of walking forward as in a Column Circulate. The dancers who are second or fourth in each column just walk forward in either case, since that motion would not cause them to leave their own box.