The genitive of the whole names what a part is taken from: aliquid boni "something good", horum ullus "any of these".
After neuter words of quantity (aliquid, nihil, quid, satis, parum, plus, tantum, tantundem): boni aliquid "something (of) good", tantundem vitae "the same amount of life".
After pronouns, numerals and superlatives (ullus, nemo, quisque, uterque, alter, unus) with a genitive plural: ab horum ullo "by any of these", reliquorum siquid "if any of the rest".
Translate with "of", or, when the genitive is a neuter adjective, as a plain adjective: aliquid boni "something good", nihil novi "nothing new".
With numerals and some pronouns, e, ex or de + ablative may replace it: unus ex multis "one of many".