In the simple case, a couple stayed married and had lots of kids (back when there was little else to do for fun, and no reliable means of contraception) there was no need to have a word for father or mother of a large family, as it was not unusual. Even now, this is the norm in some areas of society (Catholics and Mormons are stereotypical examples). A married woman who gets pregnant as often as possible is referred to as barefoot and pregnant or sometimes a baby factory or a breeder. These are all derogatory.
In traditional terms, when monogamy, cohabitation and marriage were assumed, serial partnerings resulted in step-fathers, step-mothers, half-brothers and half-sisters.
Outside of that paradigm of matrimony, nomenclature gets a bit cloudy (although half-brother and half-sister are still accurate).
note: There's a certain amount of inherent asymmetry, in that you can't always prove who is the biological father (or used to couldn't) but there is rarely any doubt as to who is the biological mother.
If one woman has children by different fathers whom she did not marry, and does not live with, those men are baby daddies to their respective offspring, regardless of the number of children.
If one man fathers children by different mothers whom he did not marry, and does not live with, those women are baby mommas to his offspring, regardless of number of children.
If a man sires many children, each with a different baby momma, I would call him a seed-sower (i.e., he has been sowing wild oats.)
Origin of phrase "sow wild oats"
If a woman bears many children, each conceived with a different baby daddy, you could call her a "serial baby momma". (That's derogatory, but not so derogatory as "slut". Of course, a [slut/ ho/ promiscuous woman/ sexually active female] might have lots of partners but no babies)
If a "baby daddy" disappears (whether by his choice or that of the baby momma), and plays no part in bringing up his offspring, he becomes what was once called an absentee father. Such a man is in legal terms a biological father, or colloquially, biological dad (sometimes more bluntly referred to as a sperm donor.) If the state keeps up with him and can keep him paying child support, he is a child-support payer. If not, he is a deadbeat dad.
If a man maintains a polygynous household, where multiple children born of several different wives are raised as his own, he is the patriarch of that family. Brigham Young, for example, was such a patriarch. (polygamy is no longer legal, nor sanctioned by the LDS church, but a few isolated splinter groups still practice it.)
I don't know of similar examples from polyandry, but I suppose by parallelism that the one mother in a polyandrous household with multiple husbands would be called the matriarch.