  We present some problems and results about variants of sunflowers in families
of sets. In particular, we improve an upper bound of the first author, K\"orner
and Monti on the maximum number of binary vectors of length $n$ so that every
four of them are split into two pairs by some coordinate. We also propose a
weaker version of the Erd\H{o}s-Rado sunflower conjecture.
