Here is the bigger picture.
We can see the dinosaur branch that simply went extinct, and the pterosaur branch that leads to birds.
Here is a cladistic analysis, which confirms the placement of Oviraptors (eg. Hagryphus, Conchoraptor) and Alvarezsaurids (eg. Mononykus, Shuvuuia)
within Paraves:
Here is the TNT input file, which is based on the data from:
A Jurassic ceratosaur from China helps clarify avian digital homologies (2009)
http://www.nature.com/articles/nature08124.epdf?referrer_access_token=1LIOYM249T2ALXmHhUVXQtRgN0jAjWel9jnR3ZoTv0NAxxXDTxDgb7tt7vNCs5i7CDx_p1E8pIL0dPMGIw0CIZ1LRnUZIDT1a3FIDY_UW4FRwpODRDVwWg-KbK448VK63yIXiGAa_H8fA42yVK8TsNhr_ASjWKKTbM-PJCMVzpKKElR4FEstewHl9DZGaHr9&tracking_referrer=www.nature.com
http://www.nature.com/nature/journal/v459/n7249/extref/nature08124-s1.pdf
xread
517 17
Euparkeria
???0000?0?000???00?0?00000000000000000001??00000000000?0?1000??0
??00?00?0?000?00?0000?0?0?0?0?000?0???0??00??0?0?001?0?000????????0030?01?0??000?1
0200?0?10?001?00000100000?0???0?0000?000???0???00?000?0??0??00??0010?00????????0??
???????????0?????0???0??0?00?00?????10?0????0???0???????000?0???????00??00?????00??0?
??00110010???00?0?0?0???0?0???????0?0000??0?00?????????0???0?0??0?0????0???0?0??????
?????????????????????????????????????????????????????????0??????????????????????????????
????????????????????????????????
Marasuchus
????
????????????????????????????????????????????????????????????????????????????????????
????????0000?00--0??001???0?00?0??0?????????????????????????????????????????????0?????
????00000?00?000--?00?00??1??0?0?0?00?20000?0?0??0?0??00000000000??????????0????01?
00?????10?0????????0???????000002-?00?00000000-0?000000-??00000011?4?00-20000-0?000
002?010000000000?00??00000000010000000?0000000?01??????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????
??????
Allosaurus
???0?0100101?0000?000?10?010?0??0??0????11??00000111?0??11001000?
00??010???0?00010001120?00010??001001100?0011000??011001?10?0000000000010010?1?0
00001010100102000000102000000000102120010000111000101100001001100100300000?00?
0?0110100101010000?1??10??00010110000000000000000100000??01001110000000?0000100
100000000100?1100001000011000000?000101000100011010001012?0?10000001101110?0020
00000?020000000010201111000000111200?100113100000010001110002000104?10?0010001
00000000000???????????????????????0???????????????????????
Compsognathus
0??00100
0???1010?1?0??201000?00?00??0000??000000000010???10110???000?001000??????
?0?????????????0?????1????????????00?????????????00000010010?0?000?1210?1??101001001
10200000000010??1??00?00111?00?????10001??110?023????0?00?0?00?10000010010100???1
???0001010?000000?1???????0?0000?????010100??0???0?0?1???????00?011??0100001000001
0000?0??1?????0000?1???1??0??????0??0?0001??10?0000200?000?0200??0010102??101000??
?1012?1?010113?0000000???0000?10010104?00?0110???0000??????0???????????????????????
0???????????????????????
Tyrannosaurus
???100000011101011101100000000001110010?00221000001110??1111010
0
0001?111
22?010100100103?00001000001001110?00100001101?01?010?02000000000100101
1?0110010101011010001001020000000001021200000001111?0100100001001100000310?00?
10?0?0?0001001111000001??11??00010100000001001001?00100010?1?0?01111100000?0110
10110000001010001100001000001021000?101101001200011010001012?20??0100020110100
0020000100020000000010200111000000111200?0001131002000100010100000001?0?00?101
0?0?02????????0???????????????????????0???????????????????????
Confuciusornis
011?1
?1?0000???????0???0?110???????0????1???1?00??0?????10-??0?0?10??000?????0?00001
?????????0??0?????????????1?????0?????????????00100000010?1?000?0???000?11-????1?????
2??????????????????0?????????0100???1?????0?5????0?21?-?1?????????????011?21?010?0???
??0?11114020????1111???0?11?11?002???0?1?1??????02??100?30-?1???00101????1?211011?1
1????2??1?10???0?1????????01??1??20???11?0?01?10??0?00??000?0-----------------------1?2??1
110?0???020??0-10?1?3??0000?0???11????200?1?4??0-0110???000???120?0?????????????????
??????
Jeholornis
????
??????0????????????????????????0?????????????????????????????????????????????1??0??
????????????????????????????????????10?????00?????????????????????????1?????1????????2?
???????????????????????????0?????2?????3???1???0?2?2???1???????????0???????1?????1??10
11[04]0????????1?1??????110?012?0??0??1?????????????????????????????????????1??1??????
??????????????????????????????????????????????????000?0-----------------------102??01100????
???200-000113?000000???????0003000104??0-0110??????00030000-----------------------
Shuvuuia
???0?011000010101?1010200000?000000000001100-1111-10111011001000-100000100010000
00010-??01?120000021101000100110??100010??110121000010001000001001110??0000?1??0
1??02--210011?1?2010?1121111?1110101010100??01?011?0?502??1120111211100200?11100
10?20??002000-1000000030001011-0001100???1?1?010?2-?111????2??111?000?20-2?1??0000
0?0??-?22000-01??11121?1010011??1???1121??1011122110?0000200102000?001101120-------
----------------1?2??2200?1000101211-1111?3??0200?01?0000???301?1????1-10?10?1000????01
?????????????????????????
Mononykus
?
???
????????????????????????????????????????????????????????????????????????????????????
??????????????????????100??????????1012?0???????????????????????????????????2--?1?0?1??
0????????1?11?0--?101?10101???1?011?0??????11?01?12?1????????????1??20??002000-?00?0
000300010?1-00011?1?1?1?1?0?????0??????????111??00?2????1??00?00?0??-?????0-?1????12
1?101001?101????1?1??1011??21???0000200102000?000101120-----------------------112112200?
1000101?11-1111????0200?01?0000?????1?1????1-10010?1000?????1???????????????????????
??
Gallus 0
110102
10?00??????101????????0??0000?100??0201111?000?1110-100?01?????01?00100?0??
?1??????012??101----0???????100?101??0?1??????????????????????????????????11-----1-----2-
-------11011200111111?0?10111100001101?101701110031?-???????????????001?2111103010-
10011011111010111101110011?1?1101012-00101?01???0210111?30-2--2?10031201011?211??
?1101112--11101010?110121?11???111???101110020011??01?001002--0-----------------------10
2?1121000001010200-02111210000000000000000-3--101-00?011?00?00?000----0----------------
-------
Conchoraptor
??????00
111
0?0?00??1???0?020???????1????1???111?000??12?10-?1000010??001?????000000
0?????????1??1?????????0????1??????00??11?????0212000201?0?0?000?0???101011-????1???
??2????-?????????0????????????1???01??0????????11??0??????1????????????0???????1?11?01
??0??010001??????001????????????010?1?001?1??????0210000?1100?1??20??1???010??000-0
??????11?1010?010?0????????????0????????0?0?00?00??0?0???10000-----------------------102??
1?1000?0?11110?-110113??000000?0?10?00?0010104??0-0010?0?00000?00100-------------------
----
Microraptor
0100?01000??1??????0??00????????00?0????????1??0??????????????????????0???????????????
??????????0??????????????????????????????????0?00010??????01??1??????010???1?01--210?0
000?0????2???011?????????0?100?0?1?00??014???1??10?1?1??1--1-0?1??2011?01101??0????1
??1111011???0??11???00??1100?111?11??1?1??????02011?1?21110?2001131?0?011111010?1
?????11?1111??10?0?????????0?0???01???1000010?11?01?11?010000-----------------------10???
???????0????2?0??0010????????????????????0011???????0????????????0?0-----------------------
Hagryphus
????
????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????
???????????????0?110???????????????????????????????????????????????????????????????????
??????????????????????????????????????????10000-----------------------1020001100000011010?-
0001131000000100010000?200?104-00-011010100000?00000-----------------------
Dilong
10?100
0?011
?10100110?1000?0001001010000001221000010110?0010001000000000120001?1
0010011??0?????00001001100000???1??1?100??0????????000000100001111111010101?1101?
00100102000000000????1?00??0?1?1??0100?????1?????0101????????????0????1?001????000?
??????0????01000?01??10001???????????????1?1?00000??0?10100100?0?0??11?????????0????
?0??0????11?110001?00??010001?12?201???00020111??0????0?00?0?2?0??000?1?2??1010?00
?011?2???00?1?3??0000?10?010????000?1?4??000010???000???120?????????????????????????
????????????????????????
Epidexipteryx
??-????????????????????????????????0???????????0000???????0?0??00?????01?1???????00?0?
???????????????????????????????????????????1??00??00????1?00??????0????0??11002???011?
1???00??????????0????????0??00?0???0????14????1?20?2????1??2????????10?1?????1?1???0?
100?1002????0000????1??????????0??????????1???????0??00??????0?00102????210?0??1????
????1???????????????0?????1??01???11102????0??0?????001???????????????????????????????
?????????????0??????????????????????????????????????????????????????????????????????????
??
Epidendrosaurus
????????????????????????????????????????????????0100?0
??????1??00?????0????????????????
???????????????????????0???????????????????21000000100?1?00?10???0????????????????1???
?
????????????????????????0?00?0?0?01???13???0??10?1????10?0???1?1????1??????101?????1
?0110?2????00?0?0??1?1?110????0??0?1?????1???????0?000??????0?00??2????2?0?0??1?????
2?2?0100????0??????0???????????????1020??00??0?00??001?0-----------------------102??????0??
??????00-00?103??0?0000?0??0?000000?114?00-0000?0?00?100200?0-----------------------
Sinosauropteryx
1000
000
001?01??0?0????00000??0?000??0?????????00??00?0???10???????0??00????0??00012
?10??????????0??????????????0??????????????????00?00?100??????????????1??101001001102
000000000????1??01?10111?10?????10?01??2?0??13??????00?0?0??1110?0111101000??????0
0010100100000?00?00???0?0000??110010100??0???0?0?101020?000?111??1??0001000011?00
0?0??1??010001??0??01??01??1??00?0?00?201101000020??00?00200??000010201221001?0?1
112?1?11010300000000???1000?10010104?00?00100?100000000100???????????????????????0
???????????????????????
Important note (not directly related to the above):
Be aware that [cladistic analysis] programs can give different answers (trees) depending on the order in which the sequences appear in the input file. PHYLIP, PAUP and other phylogenetic software provide a ‘‘jumble’’ option that reruns the analysis with different (jumbled) input orders. If for whatever reason the tree must be computed in a single run, sequences that are suspected of being‘‘problematic’’ should be placed toward the end of the input file, to lower the probability that tree rearrangement methods will be negatively influenced by a poor initial topology stemming from any problematic sequences.
Algorithms that perform optimization tasks (such as building cladograms) can be sensitive to the order in which the input data (the list of species and their characteristics) is presented. Inputting the data in various orders can cause the same algorithm to produce different "best" cladograms. In these situations, the user should input the data in various orders and compare the results.
Using different algorithms on a single data set can sometimes yield different "best" cladograms, because each algorithm may have a unique definition of what is "best".
Because of the astronomical number of possible cladograms, algorithms cannot guarantee that the solution is the overall best solution. A nonoptimal cladogram will be selected if the program settles on a local minimum rather than the desired global minimum.[14] To help solve this problem, many cladogram algorithms use a simulated annealing approach to increase the likelihood that the selected cladogram is the optimal one.[15]