  Given a scheme over a field endowed with a strict normal crossings divisor,
we define strongly parabolic connections, consistently with the current
terminology for Higgs bundles. When the weights are rational with prescribed
denominators, we show that strongly parabolic connections correspond to
holomorphic connections on the corresponding stack of roots. We use this
correspondence to establish that a holomorphic connection on a stack of roots
can be reconstructed from its direct image to the moduli space.
