Urgot vs Mordekaiser Top Matchup
Urgot Top wins 47.3% of 2,263 Low Elo games against Mordekaiser Top, -1.7 points vs expected, 2-patch window 26.19-26.20.
Researched on LoL patch 26.20. Tips are written to hold at any rank; stats come from Low Elo ranked games up to patch 26.20.
Why Mordekaiser is favored
Realm of Death(R) reaches farther than Urgot's Purge(W), so Mordekaiser can start an isolated duel before Urgot's main sustained-fire ability reaches him. Mordekaiser's stat steal and shield make an even extended fight difficult for Urgot, who is better off chipping and disengaging until Mordekaiser has spent key abilities.
How to play as Urgot
Chip Mordekaiser with Corrosive Charge(Q) and basic attacks before committing; after level 6, avoid starting a full-health duel while his Indestructible(W) is ready unless you have a clear lead.
Inside Realm of Death(R), save Disdain(E) to dodge Mordekaiser's Q or E and create space; use Fear Beyond Death(R) only when Mordekaiser is close to its execute threshold.
Realm of Death(R) reaches farther than Urgot's Purge(W), so Mordekaiser can begin a duel outside Urgot's W range.
How to play as Mordekaiser
Look to cast Realm of Death(R) from outside Purge(W)'s range when Urgot has spent Disdain(E); the extra cast range can start the duel before his sustained fire reaches you, while holding E for his next reposition helps keep him in range.
Sources
These notes come from r/UrgotMains and r/MordekaiserMains, checked against the champions' abilities.