Is it true that children's blood group is more similar 2 their mother's blood group?

well...i'd say yes...i am blood type o positive and all 3 of my kids are o positive....

not true.
I heard a case:
father is A
and mother is AB

the offspring is O.

It is possible with a factor: Bombay phenotype

No. Blood group and type is determined by both the mother and father. Here is a simplified explanation of how it works. There are 4 blood groups: A, B, AB and O. The types are either either Rh+ or Rh- , with Rh+ being dominant. The genotypes of the groups show as the following:
A can be AA, AO
B can be BB, BO
AB can be AB
O can be OO
Out of the blood types O is recessive, so in order for the child to be O both parents have to be carriers of the gene. For example if one father is AB, then the child cannot be O even if the mother is. With that example the child could only be either A or B blood type.
I hope this didn't confuse the issue more for you... genetics can get quite confusing until you understand it. Feel free to contact me if you want further explanation.

It is going to be a random combination between the father's genotype and the mother's genotype. O is recessive, A and B are co-dominant.

either or combined

Not necessarily. It is inherited like all other genetic traits with one component from each parent. There isn't any predominance towards either parent per se. It may happen that a child can have the same blood type as their mother (ie, my father is b neg, my mother is o neg, I'm o neg. However, I could have just as easily been b neg as well).

should be either mother or father or combined