baby
be someone's baby (of a project) be instigated and developed by one particular person; be someone's creation or special concern. informal
be left holding the baby: seeholding.
tar baby: seetar.
throw the baby out with the bathwater discard something valuable along with other things that are inessential or undesirable.
☞This phrase is based on a German saying recorded from the early 16th century but not introduced into English until the mid 19th century, by the Scottish historian and philosopher Thomas Carlyle. He identified it as German and gave it in the form, 'You must empty out the bathing-tub, but not the baby along with it.'
2009Erica BartleGirl with Satchel We last redesigned when we went bimonthly in 2004 and while we haven't stood still since then, we just felt a bit of a refresh was due. We have endeavoured not to throw the baby out with the bathwater, and there are lots of things we have left the same.
wet the baby's head: seewet.