It appears that despite separating some time ago, Chris Martin and Gwenyth Paltrow are yet to legally " uncouple" (divorce!)
This report suggests the divorce is yet to finalise as Chris has not completed the paperwork to enable Gwyneth to finalise the divorce.
I would be very surprised if this were the full story, as one spouse not wanting the other to remarry is never sufficient to prevent the divorce from progressing. If the divorce were based on Chris' unreasonable behaviour, evidencing the petition had been received by him would be sufficient for Gwenyth to move the divorce to the next stage.
Once divorced, it is not possible for a spouse to stop an ex remarrying, and the divorce will normally be able to move forward at the pace agreed between the parties or at one spouse's instigation if they cannot agree.
What is much more common is for the final stage of the divorce (Decree Absolute) to be delayed until the financial issues have been resolved, which can take time if there is a significant dispute about the division of assets.
The truth is, Chris stalling on signing documents is very much a calculated move to stop Gwyneth remarrying. He’s just not ready to let her go.