Personally I do believe that Tyrian is IK's daughter and that IK definitely was a playboy in his younger days. But we all have done things in our youthful days that we won't be proud of, if mentioned today. And there is a lot of evidence that IK transformed somewhat after his mother's death; at least to the extent of shunning his playboy past(although he is still a `dil phaink` as clear from his marriage with RK). Having said this:
1) The LA court judgement they so often talk about is was ex-parte judgement in a foreign country. Ex-parte judgement is when one party does not show up in the court, the court without hearing decides in the favor of other party. The repercussion for this is IK can take legal defense that he was neither resident or national of US for him to be able to follow the case in US jurisdiction.
2) About Jemima becoming care-taker of Tyrian following Sita White's death. The legal defense is both had already been divorced when this happened. And that Sita White & Jemima's father were close friends and since Sita was dieing due to cancer it was out of human compassion that she became care-taker of Tyrian.
3) Sita White is dead to so its impossible to prove any sort of relation between them now.
4) Any comments by IK in book or interview on lines of: `I have never claimed to be an angel` can be dismissed as being general remarks and not statement about a particular event.
5) All of this is not new knowledge and there was reference in ECP to this regards(which was dismissed). Similarly this argument has been brought forth each time IK has filed nomination papers in the past. Hence any case in SC can portrayed as an `attempt of revenge` against a political rival.
6) Only possibility of something coming out of this issue is if Tyrian herself becomes party to the case. Now that's not likely for now as Jemima will have considerable influence on her and she isn't a resident of Pakistan. In future, IK's political rivals may attempt to encourage her by offering monetary benefit. But PML-N may have that sought of resources but ex-CJ definitely does not have such resources. Also if she gets/enjoys a share of Jemima wealth she may not be easily incited as Jemima is herself super-rich. Even dis-regarding all these per-requisites, mother-less DNA Paternity Tests are less conclusive so a good lawyer may get the report to be dismissed on technical grounds.
So in short nothing is going to happen for now. So ex-CJ can have his 5 mins of fame and that's it.