The BAUMs of Kurima
BMD records from Kurima (films 1792393-394), which are available only from 1851, are in yellow background.
Records from the 1869 census (film 623099) are in blue background.
See footnotes, marked by green letters
Mosko BAUN (a) 1828 census, one other occupant between 18 and 60 - probably his wife
No documents connecting Mosko to anyone else, but he is probably the father of some or all
Mendel BAUM (j) (1817-53) and Feigl
Jacob Schia 1851
Isack BAUM (1816-87) and Rifke NEUMAN
Perl 
Zipsra? 1857
Ro"sy 1860
Blima 1863
Lotti 1866
Isack BAUM (b. 1817) and Rezsi GOLDBERGER (b. 1830)
Reizl 1861
Blima 1864
Abraham BAUM (1825-1904) and Eszter BAUM (1842-1898), Mosko 1858 (i)
Mendel 1867
Salomon 1869
Additional children from Homonna records:
Samuel 1876
Marjem 1872-78
Beile Frimet 1883-84
David BAUM and Malka
Lische 1854
Moses BAUM and Maly SCHONFELD
Lazar 1866 (b)
Moses BAUM (b. 1845) and Maly SCHONFELD (b. 1845)
Peschla 1863
Josef 1864
Gitlya 1866
Sandlya 1867  (h)
Abraham WEIL and Reichel BAUM (daughter of Emanuel) m. 1867 (f)
Josef RUBIN and Minda BAUM (g) David 1877
Tobi 1879
Beila 1882
Izrael 1886 (c)
Mosco 1888
Sali 1894
Osais MENDEL (b.~1832) and Perl BAUM (d)
Osias
Joszef BAUM and Maria STERN
Azriel 1887-87
Chayim 1888
Sara 1892
Herschel 1893 (e)
We also have deaths of Rachel (age 12, 1855) and Szeindel (age 5, 1856).  We don't know who their parents are.
Notes:
(a)  This is not a typo.  The actual record says BAUN, which I am assuming to be BAUM.
(b) Witness for this naming is Abraham Baum.  This is likely Abraham-Yaakov who is David's father.  Avraham-Yaakov's father and grandfather are David-Leib and Samuel respectively, according to a non-Baum descendant of my acquaintance.  I don't yet have anything connecting these people to Kurima or to any of the other Baums on this page.  However there may be a connection to Avraham Yankel, who lived in London.
(c) Mohel for this birth is Moses Baum
(d) This is according to their marriage record.  Witnesses to the marriage are Abraham Baum and Isack Baum.  On the other hand, in their son's birth record, they are called Perl Baum and Jacob Mendel.  This matter is unclear.
(e) We have Holocaust listings for Herschel, his wife and children.  In his birth record, Herschel's given name is "Szumer."
(f) I have placed Reichel below Mendel as though she is his daughter, because of space limitations, but this Mendel and this Emanuel may indeed be one and the same.
(g) I have found Pages of Testimony for Izrael from his granddaughter, Minda from Sali's son and another son Emanuel from two sons and will try to contact them soon.  Three of the four were submitted in the last fifteen years.  Three live(d) in Israel and the fourth in Michigan.
(h) Also in this census record is Chaja, surname unknown, born 1852.
(i) Mosko was probably the son of a different mother and quite possibly Abraham's two wives were related. Eszter's name Baum is from Mendel's 1887 marriage record. 
(j) We have a probable grave for Eszter BAUM (Abraham's wife) with father Menahem.  That may be this Mendel.