OK, as I've focused a bit on Australia in TDL, I might as well do a list.
The elections are in small text because the Coalition is long-ass to type up.
Prime Ministers of Australia recognised by all states and the United Nations
Malcolm Turnbull (Liberal/National/Liberal National/Country Liberal coalition) 2015-2018
2016 (maj.): def. Bill Shorten (Labor), Richard Di Natale (Green), Nick Xenophon (Xenophon Team), Bob Katter (Katter's Australian)
Bill Shorten (Labor majority) 2018-2025
2018 (maj.): def. Malcolm Turnbull (Liberal/National/Liberal National/Country Liberal coalition), Richard Di Natale (Green), Nick Xenophon (Best), Bob Katter (Katter's Australian)
2021 (maj.): def. Julie Bishop (Liberal/National/Liberal National/Country Liberal coalition), Nick Xenophon (Best), Larissa Waters (Green)
2024 (maj.): def. Christopher Pyne (Liberal/National/Liberal National/Country Liberal coalition), Rebekha Sharkie (Best), Larissa Waters (Green)
Chris Bowen (Labor majority) 2025-2027
Christian Porter (Liberal/National/Liberal National/Country Liberal coalition) 2027-2030
2027 (maj.): def. Chris Bowen (Labor), Larissa Waters (Green), Rebekha Sharkie (Best)
Amanda Rishworth (Labor minority supported by Greens) 2030-2032
2030 (min.): def. Christian Porter (Liberal/National/Liberal National/Country Liberal coalition), Adam Bandt (Green), Rebekha Sharkie (Best)
Christian Porter (Liberal National/Country Liberal coalition) 2032-2037
2032 (maj.): def. Amanda Rishworth (Labor), Adam Bandt (Green), Yvonne Chang (Best), Tim Parnell (National Country)
2035 (maj.): def. Tom Shelley (Labor), Emilia Edwards (Green), Tim Parnell (National Country), Yvonne Chang (Best)
Frankie Lewis (Liberal National/Country Liberal coalition) 2037-2046
2038 (maj.): def. Tom Shelley (Labor), Tim Parnell (National Country), Yvonne Chang (Best), Emilia Edwards (Green)
2041 (maj.): def. Paul Jenkins (Labor), Jak Rose/Benji Kennedy (Green/Best Alliance), Tim Parnell (National Country)
2044 (maj.): def. Bob Cardley (Labor), Tim Parnell (National Country), Jak Rose (Green), Benji Kennedy (Best)
Amelia Lo (Labor majority, then All-Australia Alliance, then Labor majority) 2046-2056
2046 (maj.): def. Frankie Lewis (Liberal National/Country Liberal coalition), Tim Parnell (National Country), Ed Caffley (Best), Jak Rose (Green)
2055 (maj.): def. Frankie Lewis (Liberal National/Country Liberal coalition), Tim Parnell (National Country), Ed Caffley (Best)
P. J. Sinclair (Labor majority, then Progressive/Liberal National/Country Liberal/Continuity National coalition) 2056-2063
2057 (maj.): def. Azucena Miles (Liberal National/Country Liberal/Continuity National coalition), Ed Caffley (Best)
2060 (maj.): def. Mark Branting (Labor), Ed Caffley (Best)
Azucena Miles (Liberal National/Progressive/Continuity National/Country Liberal coalition) 2063-2065
2063 (maj.): def. Mark Branting (Labor)
P. J. Sinclair (Progressive/Liberal National/Continuity National/Country Liberal coalition) 2065-2066
Chastity Bolt (Labor majority, then Labor/Progressive Left coalition, then Labor majority) 2066-2073
2066 (maj.): def. P. J. Sinclair (Progressive/Liberal National/Continuity National/Country Liberal coalition)
2069 (coal.): def. Azucena Miles (Liberal/Progressive/National/Country Liberal coalition), P. J. Sinclair (Progressive Left)
2071 (maj.): def. Joe Sharpie (Liberal/Progressive/National/Country Liberal coalition)
P. J. Sinclair (Labor majority) 2073-2075**
2074 (maj.): def. Joe Sharpie (Liberal/Progressive/National/Country Liberal coalition), committee (Flux)
Julian Daniel (Liberal/Progressive/National/Country Liberal coalition supported by Flux) 2075-2076
2075 (min.): def. P. J. Sinclair (Labor), committee (Flux)
P. J. Sinclair (Labor minority supported by Flux) 2076-2078
Julian Daniel (Progressive-Liberal/National/Country Liberal coalition) 2078-2084
2078 (maj.): def. P. J. Sinclair (Labor), committee (Flux)
2081 (maj.): def. Abby Bloom (Labor), committee (Flux)
Melody Hsu (Labor majority, then minority) 2084-2086
2084 (maj.): def. Julian Daniel (Progressive-Liberal/National/Country Liberal coalition), committee (Flux)
Julian Daniel (Progressive-Liberal/National/Country Liberal coalition) 2086-2091
2086 (maj.): def. Melody Hsu (Labor), P. J. Sinclair (People-Justice-Socialism), committee (Flux)
2089 (maj.): def. Melody Hsu (Labor), committee (Flux), P. J. Sinclair (People-Justice-Socialism)
Liam Brooke (Progressive-Liberal/National/Country Liberal coalition) 2091-2095
2093 (maj.): def. Tammy Lee (Labor), P. J. Sinclair (People-Justice-Socialism), committee (Flux)
Forrest Mander (Labor/People-Justice-Socialism coalition, then Labor majority) 2095-2098
2095 (coal.): def. Liam Brooke (Progressive-Liberal/National/Country Liberal coalition), P. J. Sinclair (People-Justice-Socialism), committee (Flux)
Liam Brooke (Progressive-Liberal/National/Country Liberal coalition) 2098-2102
2098 (maj.): def. Forrest Mander (Labor), committee (Flux)
2101 (maj.): def. P. J. Sinclair (Labor), committee (Flux)
Kim Sanders (Progressive-Liberal/National/Country Liberal coalition) 2102-2110
2104 (maj.): def. Menzies Moore (Labor), committee (Flux), Oliver Twist (End Poverty Now!)
2107 (maj.): def. Frank Reed (Labor), Oliver Twist (End Poverty Now!), Joe Martin (Shooters, Scavengers and Motoring Enthuasists), committee (Flux)
Carly Arco-Iris (Labor majority, then All-Australia Alliance) 2110-2124*
2110 (maj.): def. Kim Sanders (Progressive-Liberal/National/Country Liberal coalition), Oliver Twist (End Poverty Now!), Joe Martin (Shooters, Scavengers and Motoring Enthuasists), committee (Flux)
2113 (maj.): def. Dan Rodham (Progressive-Liberal/National/Country Liberal coalition), Joe Martin (Shooters, Scavengers and Motoring Enthuasists), committee (Flux)
Kim Sanders (All-Australia Alliance (Progressive-Liberal)) 2124-2128
Ed Mackenzie (All-Australia Alliance (Labor)) 2128-2142
William Chong (All-Australia Alliance (National)) 2142-2144
Taylor Jacobs (All-Australia Alliance (Progress)) 2144-2156
Prime Ministers of Australia as recognised by the United Nations and the states of Victoria and Tasmania (Hobart)
Chloe Curran (All-Australia Alliance (Progress)) 2156-2177
Nicky Takamine (All-Australia Alliance (Labor)) 2177-present [UN-led negotiations are ongoing]
Prime Ministers of Australia as recognised by the states of New South Wales and South Australia (Canberra)
Henry Edwards (All-Australia Alliance (Progress)) 2156-2163
Eliza Wong (All-Australia Alliance (Labor)) 2163-2174
Jacob Jacobs (All-Australia Alliance (National)) 2174-present [UN-led negotiations are ongoing]
Prime Ministers of Australia as recognised by the states of Queensland and North Australia (Brisbane)
Alison Wilde (All-Australia Alliance (National)) 2163-2179
Pauline Rees (All-Australia Alliance (Progress)) 2179-present [UN-led negotiations are ongoing]
Prime Ministers of Australia as claimed by the Shooters, Scavengers and Motoring Enthuasists Party (Alice Springs)
Note: The people labelled here as Shooters, Scavengers and Motoring Enthuasists are ones the party claims are members, but the evidence is very dubious.
"Lord Humungus" (Shooters, Scavengers and Motoring Enthuasists) 2129-2141*
in dispute (First Scavenger Civil War) 2141-2147
"Feral Kid" (Shooters, Scavengers and Motoring Enthuasists) 2147-2149*
in dispute (Second Scavenger Civil War) 2149-2163
"Aunty Entity" (Shooters, Scavengers and Motoring Enthuasists) 2163-2167*
- Savannah Nix (Independent) 2167-2168 [Recognised as the "official leader" of the Scavengers. Willingly surrendered to NSW]
- in dispute (Third Scavenger Civil War) 2167-2173 [Nix was not recognised as Prime Minister by most Scavengers]
"Immortan Joe" (Shooters, Scavengers and Motoring Enthuasists) 2173-2181*
"Imperator Furiosa" (Shooters, Scavengers and Motoring Enthuasists) 2181-present [UN-led negotiations are ongoing]