Basically, it has boiled down to whichever of the candidates at the split national convention the state party recognized. Hence while in theory, Barack Obama was the candidate of the Democratic National Committee, in actual law it was the 51 individual state parties that put his electors on the ballot. If one of those parties had decided to break with the DNC and put someone else on the ballot, then maybe a lawsuit at the state level would have worked and maybe not, but it would have depended upon the electoral law in that state the by-laws of the state party.
However, with no major party requiring a supermajority of delegates any longer, the chance of a hopelessly split convention is quite remote. What is more likely is examples such as 1948 and 1912 where state parties split from the national party and did not nominate the person the national party called for. (For instance, in South Dakota in 1912, Roosevelt was listed as the nominee of the the South Dakota Republican Party and Taft wasn't even on the ballot.)
Though it should be noted that in 1948, a number of Democratic Parties in the Deep South officially backed the States Rights ticket rather than the regular ticket, and as such Thurmond was listed as the Democratic candidate.
Today, I suppose it would depend on who communicates to the state who the party's ticket is. Is it a figure from the state party or the National party?
This map from Wikipedia