Richard II dies in 1399

As it says on the tin, say during his invasion of Ireland in 1399, Richard II is badly wounded and dies, this happens before Bolingbroke invades. Who ascends to the throne? Does Edmund Mortimer, Earl of March ascend as the heir through primogeniture, or does Henry of Bolingbroke ascend the throne due to the 1377 entail of Edward III? Or does it lead to fighting between various factions pushing for their respective claimant?

Furthermore, in another example, say Mortimer's father Roger did not die in Ireland in 1398, but was alive and well, but Richard II still died in 1399, who would ascend the throne in that instance?
 
I suppose one might say it comes down who can get to London first, and who Edmund of Langley, Duke of York supports, after all he was left as keeper of the realm when Richard went off to Ireland after all
 
On that note, is Langley more likely to side with the grown Henry of Bolingbroke who is his nephew, and might well have an army at his back, or the child Mortimer who is a distant cousin, and is a child, though as a child, Mortimer would need a regency
 
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