Is a marriage considered to have taken place merely by joking and a non-serious agreement to marry off a young girl to the questioner's nephew, especially with no dowry specified and the statement that the matter will not be concluded until the girl grows up?

Marriage is valid even from one who jokes, if its conditions and pillars are met. However, the mentioned phrase: "We want her for your nephew" does not constitute a valid marriage contract; because it is merely a proposal. One should be cautious about joking in such matters.